Explanation Given information: The function, f ( x ) = x 2 − 8 x − 10 . Formula used: Steps to solve a quadratic equation by completing square method given that is not a perfect square trinomial; 1. Make the coefficient of x 2 unity by dividing complete equation by reciprocal of the coefficient of x 2 . 2.Take one-half of the coefficient of x , square it and add it to both sides of the new equation. 3. On one side, there will be a perfect square trinomial. 4. Use square root property and solve for x. Calculation: Consider the equation, f ( x ) = x 2 − 8 x − 10 To find the x -intercepts, set f ( x ) equal to 0 and solve. f ( x ) = 0 x 2 − 8 x − 10 = 0 Add 10 on both sides. x 2 − 8 x − 10 = 0 x 2 − 8 x = 10 Half the coefficient of x is − 4 . Square it and add on both sides. x 2 − 8 x + 16 = 10 + 16 ( x − 4 ) 2 = 26 Use the principle of square roots, x − 4 = 26 or x − 4 = − 26 x = 26 + 4 or x = − 26 + 4 x ≈ − 1.099 or x ≈ 9.099 To verify, substitute x = 26 + 4 and x = − 26 + 4 in the equation x 2 − 8 x − 10 = 0 . For x = 26 + 4 ; x 2 − 8 x − 10 = 0 ( 26 + 4 ) 2 − 8 ( 26 + 4 ) − 10 = ? 0 26 + 16 + 8 26 − 8 26 − 32 − 10 = ? 0 4 2 + 8 26 − 8 26 − 42 = ? 0 This is true

6th Edition

ISBN: 9780321848741

Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 11.1, Problem 64ES

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To calculate: The x-intercepts of f(x)=x2−8x−10 by completing the square.

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Chapter 11.1, Problem 63ES

Chapter 11.1, Problem 65ES

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Chapter 11 Solutions

Elementary and Intermediate Algebra

Ch. 11.1 - Solve: 64=y2.Ch. 11.1 - Solve: t2=10. Give exact solutions and...Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 5YT Ch. 11.1 - 6. Solve: . Ch. 11.1 - Prob. 7YT Ch. 11.1 - Prob. 8YT Ch. 11.1 - Prob. 9YT Ch. 11.1 - Prob. 10YT

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The x -intercepts of f ( x ) = x 2 − 8 x − 10 by completing the square.

Solution Summary: The author explains how to solve a quadratic equation by completing square method.

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To calculate: The x-intercepts of f(x)=x2−8x−10 by completing the square.

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Chapter 11 Solutions