Answer
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.
$p=1\pm\sqrt{26}$
