# How do you solve sqrt(56-r)=r?

Dec 19, 2016

$r = 7$

#### Explanation:

Square both sides to get

$56 - r = {r}^{2}$

Then gather terms to get

${r}^{2} + r - 56 = 0.$

This is a simple quadratic, which can be solved by the quadratic formula, or, more simply, by factoring, into

$\left(r - 7\right) \left(r + 8\right) = 0$

Setting each factor equal to zero in turn gives

$r - 7 = 0 \implies r = 8 \text{ }$ and $\text{ } r + 8 = 0 \implies r = - 8$

To check,

$\sqrt{56 - 7} = \sqrt{49} = 7$

$\sqrt{56 - \left(- 8\right)} = \sqrt{64} \ne - 8 \to$ this means that $r = - 8$ is not a solution to the original equation.