How do you solve sqrt(-10+7p)=p?

Feb 14, 2017

$p = 2$ or $p = 5$

Explanation:

$\sqrt{- 10 + 7 p} = p$

Square both sides.

$- 10 + 7 p = {p}^{2}$

Subtract ${p}^{2}$ from both sides and order the equation.

$- {p}^{2} + 7 p - 10 = 0$

Multiply all terms by $- 1$.

${p}^{2} - 7 p + 10 = 0$

Factorise.

${p}^{2} - 5 p - 2 p + 10 = 0$

$p \left(p - 5\right) - 2 \left(p - 5\right) = 0$

$\left(p - 2\right) \left(p - 5\right) = 0$

$p - 2 = 0$ or $p - 5 = 0$

$p = 2$ or $p = 5$