# Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - Guided Practice for Examples 3, 4, and 5 - Page 286: 12

The solutions are $1+\sqrt{26}$ and $1-\sqrt{26}$.

#### Work Step by Step

$4p(p-2)=100\qquad$ ... use the Distributive Property. $4p^{2}-8p=100\qquad$ ...divide each term with $4$. $p^{2}-2p=25\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-2}{2})^{2}=1^{2}=1\qquad$ ...add $1$ to each side of the expression $p^{2}-2p+1=25+1\qquad$ ... write left side as a binomial squared. $(p-1)^{2}=25+1\qquad$ ...simplify. $(p-1)^{2}=26\qquad$ ...take square roots of each side. $p-1=\pm\sqrt{26}\qquad$ ...add $1$ to each side of the expression $p-1+1=\pm\sqrt{26}+1\qquad$ ...simplify. $p=1\pm\sqrt{26}$

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