Consider the equation: x?2x – 8 = 0A) First, use the "completing the square" process to write this equation in the form (x + D)² = E and enteryour results below.x – 2x – 8 = 0 is equivalent to:=Preview left side of eqn:B) Solve your equation and enter your answers below as a list of numbers, separated with a comma wherenecessary.Answer(s):

Answered: Consider the equation: x2 – 2x – 8 = 0…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.13: Using Factoring To Solve Problems

Problem 30P

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Question

Consider the equation: x?
2x – 8 = 0
A) First, use the "completing the square" process to write this equation in the form (x + D)² = E and enter
your results below.
x – 2x – 8 = 0 is equivalent to:
=
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a comma where
necessary.
Answer(s):

Expert Solution

Step 1

Given equation is

$x^{2} - 2 x - 8 = 0 . . . . . (1)$

Step 2

Part (A)

$∵ x^{2} - 2 x - 8 = 0 \Rightarrow x^{2} - 2 x - 8 + 1 = 0 + 1 \Rightarrow x^{2} - 2 x + 1 - 8 = 1 \Rightarrow {(x - 1)}^{2} - 8 = 1 \Rightarrow {(x - 1)}^{2} = 1 + 8 \Rightarrow {(x - 1)}^{2} = 9$

i.e.

Equation $x^{2} - 2 x - 8 = 0$ , is equivalent to ${(x - 1)}^{2} = 9$

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