## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises - Page 512: 51

#### Answer

$25$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To determine the number that will complete the square to solve the given equation, $x^2+10x+18=0 ,$ use first the properties of equality to express the equation in the form $x^2+bx=c.$ Once in this form, the needed number to complete the square of the left side is equal to $\left( \dfrac{b}{2} \right)^2.$ $\bf{\text{Solution Details:}}$ Using the properties of equality, in the form $x^2+bx=c,$ the given equation is equivalent to \begin{array}{l}\require{cancel} x^2+10x=-18 .\end{array} In the equation above, $b= 10 .$ Using $\left( \dfrac{b}{2} \right)^2$, the number that will complete the square on the left side of the equal sign is \begin{array}{l}\require{cancel} \left( \dfrac{10}{2} \right)^2 \\\\= \left( 5 \right)^2 \\\\= 25 .\end{array}

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