To solve the equation graphically by finding x-intercepts. Confirm by using factoring the equation, x(3x+11)=20 .

x={−5, 1⋅33}

Given:

The equation is, x(3x+11)=20

Concept Used:

The x-intercept is given by y = 0: 0 = ax² + bx + c. Isolating the square and then applying the square root property.

The discriminant gives the number of x-intercepts of a quadratic function, because it gives us the number of solutions to ax² + bx + c = 0.

Calculation:

x(3x+11)=20 3x2+11x=20 3x2+11x−20=0

Let y=0

So 3x2+11x−20=y

The graph of 3x2+11x−20=y

is shown below:

Since the graph intersects the x- axis at x=−5 and x=1⋅33 , so the solutions are x={−5,1⋅33}

Now solve by factoring method-

3x2+11x−20=0 3x2+(15−4)x−20=0 3x2+15x−4x−20=03x(x+5)−4(x+5)=0(3x−4)(x+5)=0(3x−4)=03x=4x=43x=1⋅33(x+5)=0x=−5x={−5,1⋅33 }

Both from graphically and factoring solution is same i.e x={−5, 1⋅33 }

Thus, the solution of the given equation is x={−5, 1⋅33 }

Chapter P.5, Problem 5E

Chapter P.5, Problem 7E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

Ch. P.1 - Prob. 1QR Ch. P.1 - Prob. 2QR Ch. P.1 - Prob. 3QR Ch. P.1 - Prob. 4QR Ch. P.1 - Prob. 5QR Ch. P.1 - Prob. 6QR Ch. P.1 - Prob. 7QR Ch. P.1 - Prob. 8QR Ch. P.1 - Prob. 9QR Ch. P.1 - Prob. 10QR

Ch. P.1 - Prob. 1E Ch. P.1 - Prob. 2E Ch. P.1 - Prob. 3E Ch. P.1 - Prob. 4E Ch. P.1 - Prob. 5E Ch. P.1 - Prob. 6E Ch. P.1 - Prob. 7E Ch. P.1 - Prob. 8E Ch. P.1 - Prob. 9E Ch. P.1 - Prob. 10E Ch. P.1 - Prob. 11E Ch. P.1 - Prob. 12E Ch. P.1 - Prob. 13E Ch. P.1 - Prob. 14E Ch. P.1 - Prob. 15E Ch. P.1 - Prob. 16E Ch. P.1 - Prob. 17E Ch. P.1 - Prob. 18E Ch. P.1 - Prob. 19E Ch. P.1 - Prob. 20E Ch. P.1 - Prob. 21E Ch. P.1 - Prob. 22E Ch. P.1 - Prob. 23E Ch. P.1 - Prob. 24E Ch. P.1 - Prob. 25E Ch. P.1 - Prob. 26E Ch. P.1 - Prob. 27E Ch. P.1 - Prob. 28E Ch. P.1 - Prob. 29E Ch. P.1 - Prob. 30E Ch. P.1 - Prob. 31E Ch. P.1 - Prob. 32E Ch. P.1 - Prob. 33E Ch. P.1 - Prob. 34E Ch. P.1 - Prob. 35E Ch. P.1 - Prob. 36E Ch. P.1 - Prob. 37E Ch. P.1 - Prob. 38E Ch. P.1 - Prob. 39E Ch. P.1 - Prob. 40E Ch. P.1 - Prob. 41E Ch. P.1 - Prob. 42E Ch. P.1 - Prob. 43E Ch. P.1 - Prob. 44E Ch. P.1 - Prob. 45E Ch. P.1 - Prob. 46E Ch. P.1 - Prob. 47E Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - Prob. 50E Ch. P.1 - Prob. 51E Ch. P.1 - Prob. 52E Ch. P.1 - Prob. 53E Ch. P.1 - Prob. 54E Ch. P.1 - Prob. 55E Ch. P.1 - Prob. 56E Ch. P.1 - Prob. 57E Ch. P.1 - Prob. 58E Ch. P.1 - Prob. 59E Ch. P.1 - Prob. 60E Ch. P.1 - Prob. 61E Ch. P.1 - Prob. 62E Ch. P.1 - Prob. 63E Ch. P.1 - In Exercises 63 and 64, use scientific notation to...Ch. P.1 - Prob. 65E Ch. P.1 - Prob. 66E Ch. P.1 - Prob. 67E Ch. P.1 - Prob. 68E Ch. P.1 - Prob. 69E Ch. P.1 - Prob. 70E Ch. P.1 - Prob. 71E Ch. P.1 - Prob. 72E Ch. P.1 - Prob. 73E Ch. P.1 - Prob. 74E Ch. P.1 - Prob. 75E Ch. P.1 - Prob. 76E Ch. P.2 - Prob. 1QR Ch. P.2 - Prob. 2QR Ch. P.2 - Prob. 3QR Ch. P.2 - Prob. 4QR Ch. P.2 - Prob. 5QR Ch. P.2 - Prob. 6QR Ch. P.2 - Prob. 7QR Ch. P.2 - Prob. 8QR Ch. P.2 - Prob. 9QR Ch. P.2 - Prob. 10QR Ch. P.2 - Prob. 1E Ch. P.2 - Prob. 2E Ch. P.2 - Prob. 3E Ch. P.2 - Prob. 4E Ch. P.2 - Prob. 5E Ch. P.2 - Prob. 6E Ch. P.2 - Prob. 7E Ch. P.2 - Prob. 8E Ch. 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