# Solve for x in 2x + 20sqrt(x) - 42 = 0?

Apr 14, 2018

#### Explanation:

This may look complicated but can be solved like a quadratic equation if we let $u = \sqrt{x}$

$2 x + 20 \sqrt{x} - 42 = 0$

$2 {u}^{2} + 20 u - 42 = 0$

${u}^{2} + 10 u - 21 = 0$

$u = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$u = \frac{- 10 \pm \sqrt{{10}^{2} - 4 \times 1 \times - 21}}{2 \times 1}$

$u = \frac{- 10 \pm \sqrt{184}}{2}$

$u = \frac{- 10 \pm 2 \sqrt{46}}{2}$

$u = - 5 \pm \sqrt{46}$

Therefore:

$\sqrt{x} = \sqrt{- 5 \pm \sqrt{46}}$