Solve the equation 3x2+7x−24=13x by quadratic formula and then by factoring to check solution.

The solution for the quadratic equation is x=−2,4 .

Given:

The quadratic equation is 3x2+7x−24=13x .

Concept used:

Any quadratic equation of the form ax2+bx+c=0 where a≠0 has the roots x=−b±b2−4ac2a ......1

Calculation:

The quadratic equation 3x2+7x−24=13x is re-written as:

3x2+7x−24=13x ......Given3x2−6x−24=0 ......2

The solution for the quadratic equation 2 can be evaluated with the help of formula 1 . Therefore,

x=−b±b2−4ac2a ......From 1=−−6±−62−43−2423 ......∵3x2−6x−24=0=6±3246=6+186,6−186=4,−2

Hence the solution for the quadratic equation is s=3,−1 .

Now, factoring the equation 2 gives,

3x2−6x−24=0 ......From 23x2−12x+6x−24=03xx−4+6x−4=03x+6x−4=03x+6=0 or x−4=0x=−2 or x=4x=−2,4

From both the techniques the solutions are same for of the quadratic equation. Hence the required solution is x=−2,4 of quadratic equation.

Chapter 1.8, Problem 26E

Chapter 1.8, Problem 28E

Chapter 1 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 1.1 - Prob. 1GP Ch. 1.1 - Prob. 2GP Ch. 1.1 - Prob. 3GP Ch. 1.1 - Prob. 4GP Ch. 1.1 - Prob. 5GP Ch. 1.1 - Prob. 6GP Ch. 1.1 - Prob. 7GP Ch. 1.1 - Prob. 8GP Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E

Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55PS Ch. 1.1 - Prob. 56PS Ch. 1.1 - Prob. 57PS Ch. 1.1 - Prob. 58PS Ch. 1.1 - Prob. 59PS Ch. 1.1 - Prob. 60PS Ch. 1.1 - Prob. 61PS Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.2 - Prob. 1GP Ch. 1.2 - Prob. 2GP Ch. 1.2 - Prob. 3GP Ch. 1.2 - Prob. 4GP Ch. 1.2 - Prob. 5GP Ch. 1.2 - Prob. 6GP Ch. 1.2 - Prob. 7GP Ch. 1.2 - Prob. 8GP Ch. 1.2 - Prob. 9GP Ch. 1.2 - Prob. 10GP Ch. 1.2 - Prob. 11GP Ch. 1.2 - Prob. 12GP Ch. 1.2 - Prob. 13GP Ch. 1.2 - Prob. 14GP Ch. 1.2 - Prob. 15GP Ch. 1.2 - Prob. 16GP Ch. 1.2 - Prob. 1E Ch. 1.2 - Prob. 2E Ch. 1.2 - Prob. 3E Ch. 1.2 - Prob. 4E Ch. 1.2 - Prob. 5E Ch. 1.2 - Prob. 6E Ch. 1.2 - Prob. 7E Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Prob. 10E Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - 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Prob. 60E Ch. 1.4 - Prob. 61E Ch. 1.4 - Prob. 62PS Ch. 1.4 - Prob. 63PS Ch. 1.4 - Prob. 64PS Ch. 1.4 - Prob. 65PS Ch. 1.4 - Prob. 66PS Ch. 1.4 - Prob. 67PS Ch. 1.4 - Prob. 68PS Ch. 1.4 - Prob. 1Q Ch. 1.4 - Prob. 2Q Ch. 1.4 - Prob. 3Q Ch. 1.4 - Prob. 4Q Ch. 1.4 - Prob. 5Q Ch. 1.4 - Prob. 6Q Ch. 1.4 - Prob. 7Q Ch. 1.4 - Prob. 8Q Ch. 1.4 - Prob. 9Q Ch. 1.4 - Prob. 10Q Ch. 1.4 - Prob. 11Q Ch. 1.4 - Prob. 12Q Ch. 1.4 - Prob. 13Q Ch. 1.5 - Prob. 1GP Ch. 1.5 - Prob. 2GP Ch. 1.5 - Prob. 3GP Ch. 1.5 - Prob. 4GP Ch. 1.5 - Prob. 5GP Ch. 1.5 - Prob. 6GP Ch. 1.5 - Prob. 7GP Ch. 1.5 - Prob. 8GP Ch. 1.5 - Prob. 9GP Ch. 1.5 - Prob. 10GP Ch. 1.5 - Prob. 11GP Ch. 1.5 - Prob. 12GP Ch. 1.5 - Prob. 13GP Ch. 1.5 - Prob. 14GP Ch. 1.5 - Prob. 15GP Ch. 1.5 - Prob. 16GP Ch. 1.5 - Prob. 17GP Ch. 1.5 - Prob. 18GP Ch. 1.5 - Prob. 19GP Ch. 1.5 - Prob. 20GP Ch. 1.5 - Prob. 1E Ch. 1.5 - Prob. 2E Ch. 1.5 - Prob. 3E Ch. 1.5 - Prob. 4E Ch. 1.5 - Prob. 5E Ch. 1.5 - Prob. 6E Ch. 1.5 - Prob. 7E Ch. 1.5 - Prob. 8E Ch. 1.5 - Prob. 9E Ch. 1.5 - Prob. 10E Ch. 1.5 - Prob. 11E Ch. 1.5 - Prob. 12E Ch. 1.5 - Prob. 13E Ch. 1.5 - Prob. 14E Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Prob. 17E Ch. 1.5 - Prob. 18E Ch. 1.5 - Prob. 19E Ch. 1.5 - Prob. 20E Ch. 1.5 - Prob. 21E Ch. 1.5 - Prob. 22E Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1.5 - Prob. 25E Ch. 1.5 - Prob. 26E Ch. 1.5 - Prob. 27E Ch. 1.5 - Prob. 28E Ch. 1.5 - Prob. 29E Ch. 1.5 - Prob. 30E Ch. 1.5 - Prob. 31E Ch. 1.5 - Prob. 32E Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Prob. 37E Ch. 1.5 - Prob. 38PS Ch. 1.5 - Prob. 39PS Ch. 1.5 - Prob. 40PS Ch. 1.5 - Prob. 41PS Ch. 1.5 - Prob. 42PS Ch. 1.5 - Prob. 43PS Ch. 1.5 - Prob. 1P Ch. 1.5 - Prob. 2P Ch. 1.5 - Prob. 3P Ch. 1.5 - Prob. 4P Ch. 1.5 - Prob. 5P Ch. 1.5 - Prob. 6P Ch. 1.5 - Prob. 7P Ch. 1.5 - Prob. 8P Ch. 1.5 - Prob. 9P Ch. 1.5 - Prob. 10P Ch. 1.5 - Prob. 1MRPS Ch. 1.5 - Prob. 2MRPS Ch. 1.5 - Prob. 3MRPS Ch. 1.5 - Prob. 4MRPS Ch. 1.5 - Prob. 5MRPS Ch. 1.5 - Prob. 6MRPS Ch. 1.5 - Prob. 7MRPS Ch. 1.6 - Prob. 1GP Ch. 1.6 - Prob. 2GP Ch. 1.6 - Prob. 3GP Ch. 1.6 - Prob. 4GP Ch. 1.6 - Prob. 5GP Ch. 1.6 - Prob. 6GP Ch. 1.6 - Prob. 7GP Ch. 1.6 - Prob. 8GP Ch. 1.6 - Prob. 9GP Ch. 1.6 - Prob. 10GP Ch. 1.6 - Prob. 11GP Ch. 1.6 - Prob. 12GP Ch. 1.6 - Prob. 13GP Ch. 1.6 - Prob. 14GP Ch. 1.6 - Prob. 15GP Ch. 1.6 - Prob. 16GP Ch. 1.6 - Prob. 17GP Ch. 1.6 - Prob. 18GP Ch. 1.6 - Prob. 1E Ch. 1.6 - Prob. 2E Ch. 1.6 - Prob. 3E Ch. 1.6 - Prob. 4E Ch. 1.6 - Prob. 5E Ch. 1.6 - Prob. 6E Ch. 1.6 - Prob. 7E Ch. 1.6 - Prob. 8E Ch. 1.6 - Prob. 9E Ch. 1.6 - Prob. 10E Ch. 1.6 - Prob. 11E Ch. 1.6 - Prob. 12E Ch. 1.6 - Prob. 13E Ch. 1.6 - Prob. 14E Ch. 1.6 - Prob. 15E Ch. 1.6 - Prob. 16E Ch. 1.6 - Prob. 17E Ch. 1.6 - Prob. 18E Ch. 1.6 - Prob. 19E Ch. 1.6 - Prob. 20E Ch. 1.6 - Prob. 21E Ch. 1.6 - Prob. 22E Ch. 1.6 - Prob. 23E Ch. 1.6 - Prob. 24E Ch. 1.6 - Prob. 25E Ch. 1.6 - Prob. 26E Ch. 1.6 - Prob. 27E Ch. 1.6 - Prob. 28E Ch. 1.6 - Prob. 29E Ch. 1.6 - Prob. 30E Ch. 1.6 - 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Prob. 3GP Ch. 1.7 - Prob. 4GP Ch. 1.7 - Prob. 5GP Ch. 1.7 - Prob. 6GP Ch. 1.7 - Prob. 7GP Ch. 1.7 - Prob. 8GP Ch. 1.7 - Prob. 9GP Ch. 1.7 - Prob. 10GP Ch. 1.7 - Prob. 11GP Ch. 1.7 - Prob. 12GP Ch. 1.7 - Prob. 13GP Ch. 1.7 - Prob. 14GP Ch. 1.7 - Prob. 15GP Ch. 1.7 - Prob. 16GP Ch. 1.7 - Prob. 1E Ch. 1.7 - Prob. 2E Ch. 1.7 - Prob. 3E Ch. 1.7 - Prob. 4E Ch. 1.7 - Prob. 5E Ch. 1.7 - Prob. 6E Ch. 1.7 - Prob. 7E Ch. 1.7 - Prob. 8E Ch. 1.7 - Prob. 9E Ch. 1.7 - Prob. 10E Ch. 1.7 - Prob. 11E Ch. 1.7 - Prob. 12E Ch. 1.7 - Prob. 13E Ch. 1.7 - Prob. 14E Ch. 1.7 - Prob. 15E Ch. 1.7 - Prob. 16E Ch. 1.7 - Prob. 17E Ch. 1.7 - Prob. 18E Ch. 1.7 - Prob. 19E Ch. 1.7 - Prob. 20E Ch. 1.7 - Prob. 21E Ch. 1.7 - Prob. 22E Ch. 1.7 - Prob. 23E Ch. 1.7 - Prob. 24E Ch. 1.7 - Prob. 25E Ch. 1.7 - Prob. 26E Ch. 1.7 - Prob. 27E Ch. 1.7 - Prob. 28E Ch. 1.7 - Prob. 29E Ch. 1.7 - Prob. 30E Ch. 1.7 - Prob. 31E Ch. 1.7 - Prob. 32E Ch. 1.7 - Prob. 33E Ch. 1.7 - Prob. 34E Ch. 1.7 - Prob. 35E Ch. 1.7 - Prob. 36E Ch. 1.7 - Prob. 37E Ch. 1.7 - 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Prob. 43E Ch. 1.8 - Prob. 44E Ch. 1.8 - Prob. 45E Ch. 1.8 - Prob. 46E Ch. 1.8 - Prob. 47E Ch. 1.8 - Prob. 48E Ch. 1.8 - Prob. 49E Ch. 1.8 - Prob. 50E Ch. 1.8 - Prob. 51E Ch. 1.8 - Prob. 52E Ch. 1.8 - Prob. 53E Ch. 1.8 - Prob. 54E Ch. 1.8 - Prob. 55E Ch. 1.8 - Prob. 56E Ch. 1.8 - Prob. 57E Ch. 1.8 - Prob. 58E Ch. 1.8 - Prob. 59E Ch. 1.8 - Prob. 60E Ch. 1.8 - Prob. 61E Ch. 1.8 - Prob. 62E Ch. 1.8 - Prob. 63E Ch. 1.8 - Prob. 64E Ch. 1.8 - Prob. 65E Ch. 1.8 - Prob. 66E Ch. 1.8 - Prob. 67E Ch. 1.8 - Prob. 68PS Ch. 1.8 - Prob. 69PS Ch. 1.8 - Prob. 70PS Ch. 1.8 - Prob. 71PS Ch. 1.8 - Prob. 72PS Ch. 1.8 - Prob. 73PS Ch. 1.8 - Prob. 74PS Ch. 1.9 - Prob. 1GP Ch. 1.9 - Prob. 2GP Ch. 1.9 - Prob. 3GP Ch. 1.9 - Prob. 4GP Ch. 1.9 - Prob. 5GP Ch. 1.9 - Prob. 6GP Ch. 1.9 - Prob. 7GP Ch. 1.9 - Prob. 1E Ch. 1.9 - Prob. 2E Ch. 1.9 - Prob. 3E Ch. 1.9 - Prob. 4E Ch. 1.9 - Prob. 5E Ch. 1.9 - Prob. 6E Ch. 1.9 - Prob. 7E Ch. 1.9 - Prob. 8E Ch. 1.9 - Prob. 9E Ch. 1.9 - Prob. 10E Ch. 1.9 - Prob. 11E Ch. 1.9 - Prob. 12E Ch. 1.9 - Prob. 13E Ch. 1.9 - Prob. 14E Ch. 1.9 - Prob. 15E Ch. 1.9 - Prob. 16E Ch. 1.9 - Prob. 17E Ch. 1.9 - Prob. 18E Ch. 1.9 - Prob. 19E Ch. 1.9 - Prob. 20E Ch. 1.9 - Prob. 21E Ch. 1.9 - Prob. 22E Ch. 1.9 - Prob. 23E Ch. 1.9 - Prob. 24E Ch. 1.9 - Prob. 25E Ch. 1.9 - Prob. 26E Ch. 1.9 - Prob. 27E Ch. 1.9 - Prob. 28E Ch. 1.9 - Prob. 29E Ch. 1.9 - Prob. 30E Ch. 1.9 - Prob. 31E Ch. 1.9 - Prob. 32E Ch. 1.9 - Prob. 33E Ch. 1.9 - Prob. 34E Ch. 1.9 - Prob. 35E Ch. 1.9 - Prob. 36E Ch. 1.9 - Prob. 37E Ch. 1.9 - Prob. 38E Ch. 1.9 - Prob. 39E Ch. 1.9 - Prob. 40E Ch. 1.9 - Prob. 41E Ch. 1.9 - Prob. 42E Ch. 1.9 - Prob. 43E Ch. 1.9 - Prob. 44E Ch. 1.9 - Prob. 45E Ch. 1.9 - Prob. 46E Ch. 1.9 - Prob. 47E Ch. 1.9 - Prob. 48E Ch. 1.9 - Prob. 49E Ch. 1.9 - Prob. 50E Ch. 1.9 - Prob. 51E Ch. 1.9 - Prob. 52E Ch. 1.9 - Prob. 53E Ch. 1.9 - Prob. 54E Ch. 1.9 - Prob. 55E Ch. 1.9 - Prob. 56E Ch. 1.9 - Prob. 57E Ch. 1.9 - Prob. 58E Ch. 1.9 - Prob. 59E Ch. 1.9 - Prob. 60E Ch. 1.9 - Prob. 61E Ch. 1.9 - Prob. 62E Ch. 1.9 - Prob. 63E Ch. 1.9 - Prob. 64E Ch. 1.9 - Prob. 65E Ch. 1.9 - Prob. 66E Ch. 1.9 - Prob. 67E Ch. 1.9 - Prob. 68E Ch. 1.9 - Prob. 69E Ch. 1.9 - Prob. 70PS Ch. 1.9 - Prob. 71PS Ch. 1.9 - Prob. 72PS Ch. 1.9 - Prob. 73PS Ch. 1.9 - Prob. 74PS Ch. 1.9 - Prob. 75PS Ch. 1.9 - Prob. 76PS Ch. 1.9 - Prob. 77PS Ch. 1.9 - Prob. 1Q Ch. 1.9 - Prob. 2Q Ch. 1.9 - Prob. 3Q Ch. 1.9 - Prob. 4Q Ch. 1.9 - Prob. 5Q Ch. 1.9 - Prob. 6Q Ch. 1.9 - Prob. 7Q Ch. 1.9 - Prob. 8Q Ch. 1.9 - Prob. 9Q Ch. 1.9 - Prob. 10Q Ch. 1.9 - Prob. 11Q Ch. 1.9 - Prob. 12Q Ch. 1.9 - Prob. 13Q Ch. 1.9 - Prob. 1MRPS Ch. 1.9 - Prob. 2MRPS Ch. 1.9 - Prob. 3MRPS Ch. 1.9 - Prob. 4MRPS Ch. 1.9 - Prob. 5MRPS Ch. 1.9 - Prob. 6MRPS Ch. 1.9 - Prob. 7MRPS Ch. 1.9 - Prob. 8MRPS Ch. 1.9 - Prob. 9MRPS Ch. 1 - Prob. 1VE Ch. 1 - Prob. 2VE Ch. 1 - Prob. 3VE Ch. 1 - Prob. 4VE Ch. 1 - Prob. 5REAE Ch. 1 - Prob. 6REAE Ch. 1 - Prob. 7REAE Ch. 1 - Prob. 8REAE Ch. 1 - Prob. 9REAE Ch. 1 - Prob. 10REAE Ch. 1 - Prob. 11REAE Ch. 1 - Prob. 12REAE Ch. 1 - Prob. 13REAE Ch. 1 - Prob. 14REAE Ch. 1 - Prob. 15REAE Ch. 1 - Prob. 16REAE Ch. 1 - Prob. 17REAE Ch. 1 - Prob. 18REAE Ch. 1 - Prob. 19REAE Ch. 1 - Prob. 20REAE Ch. 1 - Prob. 21REAE Ch. 1 - Prob. 22REAE Ch. 1 - Prob. 23REAE Ch. 1 - Prob. 24REAE Ch. 1 - Prob. 25REAE Ch. 1 - Prob. 26REAE Ch. 1 - Prob. 27REAE Ch. 1 - Prob. 28REAE Ch. 1 - Prob. 29REAE Ch. 1 - Prob. 30REAE Ch. 1 - Prob. 31REAE Ch. 1 - Prob. 32REAE Ch. 1 - Prob. 33REAE Ch. 1 - Prob. 34REAE Ch. 1 - Prob. 35REAE Ch. 1 - Prob. 36REAE Ch. 1 - Prob. 37REAE Ch. 1 - Prob. 38REAE Ch. 1 - Prob. 39REAE Ch. 1 - Prob. 40REAE Ch. 1 - Prob. 41REAE Ch. 1 - Prob. 42REAE Ch. 1 - Prob. 43REAE Ch. 1 - Prob. 44REAE Ch. 1 - Prob. 1T Ch. 1 - Prob. 2T Ch. 1 - Prob. 3T Ch. 1 - Prob. 4T Ch. 1 - Prob. 5T Ch. 1 - Prob. 6T Ch. 1 - Prob. 7T Ch. 1 - Prob. 8T Ch. 1 - Prob. 9T Ch. 1 - Prob. 10T Ch. 1 - Prob. 11T Ch. 1 - Prob. 12T Ch. 1 - Prob. 13T Ch. 1 - Prob. 14T Ch. 1 - Prob. 15T Ch. 1 - Prob. 16T Ch. 1 - Prob. 17T Ch. 1 - Prob. 18T Ch. 1 - Prob. 19T Ch. 1 - Prob. 20T Ch. 1 - Prob. 21T Ch. 1 - Prob. 22T Ch. 1 - Prob. 23T Ch. 1 - Prob. 24T Ch. 1 - Prob. 25T Ch. 1 - Prob. 26T Ch. 1 - Prob. 27T Ch. 1 - Prob. 28T Ch. 1 - Prob. 29T Ch. 1 - Prob. 30T Ch. 1 - Prob. 31T Ch. 1 - Prob. 1P Ch. 1 - Prob. 2P Ch. 1 - Prob. 1TP Ch. 1 - Prob. 2TP Ch. 1 - Prob. 3TP Ch. 1 - Prob. 4TP Ch. 1 - Prob. 5TP Ch. 1 - Prob. 6TP Ch. 1 - Prob. 7TP Ch. 1 - Prob. 8TP Ch. 1 - Prob. 9TP Ch. 1 - Prob. 10TP Ch. 1 - Prob. 11TP Ch. 1 - Prob. 12TP Ch. 1 - Prob. 13TP Ch. 1 - Prob. 14TP Ch. 1 - Prob. 15TP Ch. 1 - Prob. 16TP Ch. 1 - Prob. 17TP Ch. 1 - Prob. 18TP Ch. 1 - Prob. 19TP Ch. 1 - Prob. 20TP Ch. 1 - Prob. 21TP Ch. 1 - Prob. 22TP

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What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY

Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY

Solution Summary: The author explains how the quadratic equation 3x2+7x-24=13x is re-written with the help of formula (1).

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Chapter 1 Solutions