Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - Chapter Review - Page 271: 55

Answer

$x=-4-\sqrt{10}$ OR $x=-4+\sqrt{10}$

Work Step by Step

In the form $x^2+bx=c,$ the given equation, $ x^2+8x+6=0 ,$ is equivalent to \begin{align*} x^2+8x&=-6 .\end{align*} Adding $\left( \dfrac{b}{2} \right)^2$ on both sides to complete the square of the left side results to \begin{align*} x^2+8x+\left(\dfrac{8}{2} \right)^2&=-6+\left(\dfrac{8}{2} \right)^2 \\\\ x^2+8x+\left(4 \right)^2&=-6+\left(4 \right)^2 \\ x^2+8x+16&=-6+16 \\ (x+4)^2&=10 .\end{align*} Taking the square root of both sides (Square Root Property) and then solving for the variable, the equation above is equivalent to \begin{align*} x+4&=\pm\sqrt{10} \\ x&=-4\pm\sqrt{10} .\end{align*} Hence, the solutions are $x=-4-\sqrt{10}$ OR $x=-4+\sqrt{10}$.
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