Explanation Given, The quadratic equation in standard form is, a x 2 + b x + c = 0 , a ≠ 0 To develop the quadratic formula, Let’s complete the square for this quadratic equation in standard form. First we divide both sides of the equation by the coefficient of x 2 and get the variable terms alone one side of the equation. (i.e.) a x 2 + b x + c = 0 Divide ' a ' on both sides, a x 2 a + b x a + c a = 0 a x 2 + b a x + c a = 0 Add − c a on both sides, x 2 + b a x + c a + ( − c a ) = 0 + ( − c a ) Since addition is associative, x 2 + b a x + c a + ( c a − c a ) = − c a x 2 + b a x = − c a The coefficient of x is b a Half of b a is b 2 a and ( b 2 a ) 2 = b 2 4 a 2 So we add b 2 4 a 2 to both sides of the equation. Add b 2 4 a 2 on both sides, x 2 + b a x + b 2 4 a 2 = − c a + b 2 4 a 2 x 2 + b a x + ( b 2 a ) 2 = − c a + b 2 4 a 2 Here, x 2 + b a x + ( b 2 a ) 2 is in the form of a 2 + 2 a b + b 2 = ( a + b ) 2 (i.e.) a = x and b = b 2 a (i.e.) ( x + b 2 a ) 2 = − c a + b 2 4 a 2 Multiply − c a by 4 a 4 a so that the terms on the right side have a common denominator. ( x + b 2 a ) = − 4 a c 4 a 2 + b 2 4 a 2 Since the right side has a common denominator then adding the numerator. ( x + b 2 a ) 2 = − 4 a c + b 2 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 By generalized the square root property

Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)

5th Edition

ISBN: 9780134707631

Author: Elayn Martin-Gay

Publisher: PEARSON

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Chapter 16.3, Problem 70E

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The quadratic formula is developed and why it is useful.

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Chapter 16.3, Problem 69E

Chapter 16.3, Problem 71E

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Chapter 16 Solutions

Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)

Ch. 16.1 - Prob. 1P Ch. 16.1 - Prob. 2P Ch. 16.1 - Prob. 3P Ch. 16.1 - Prob. 4P Ch. 16.1 - Prob. 5P Ch. 16.1 - Prob. 6P Ch. 16.1 - Prob. 7P Ch. 16.1 - Prob. 8P Ch. 16.1 - Prob. 9P Ch. 16.1 - Prob. 1E

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The quadratic formula is developed and why it is useful.

To explain: The quadratic formula is developed and why it is useful.

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Chapter 16 Solutions

To explain:

The quadratic formula is developed and why it is useful.