# How do you solve -3=(37-3n)^(1/2)-n?

Sep 19, 2016

n = 7, - 4

#### Explanation:

-3 = ${\left(37 - 3 n\right)}^{\frac{1}{2}} - n$
or, -3 + n = ${\left(37 - 3 n\right)}^{\frac{1}{2}}$ [squaring both sides]
or, ${\left(- 3 + n\right)}^{2} = {\left(37 - 3 n\right)}^{\left(\frac{1}{2}\right) \cdot 2}$
or, 9 - 6n + ${n}^{2}$ = 37 - 3n
or, ${n}^{2} - 3 n - 28 = 0$
or, ${n}^{2} - 7 n + 4 n - 28 = 0$
or, n ( n - 7 ) + 4 ( n - 7 ) = 0
or, (n - 7) (n + 4 ) = 0
or, n = 7, - 4