Chapter 9 - Solving Quadratic Equations - 9.4 - Solving Quadratic Equations by Completing the Square - Exercises - Page 511: 13

$=x^2+16x+64$ $=(x+8)^2$

The given expression is $=x^2+16x$ Find the value of $(\frac{b}{2})^2$. Substitute $16$ for $b$. $=(\frac{16}{2})^2$ Simplify. $=(8)^2$ $=64$ Add $64$ to the given expression. $=x^2+16x+64$ Write the the polynomial as $a^2+2ab+b^2$. $=x^2+2(x)(8)+(8)^2$ Use perfect square trinomial pattern $a^2+2ab+b^2=(a+b)^2$ We have $a=x$ and $b=8$. $=(x+8)^2$