How do you solve sqrt(8 + 7x) - 2 = x?

Feb 21, 2016

I found:
${x}_{1} = 4$
${x}_{2} = - 1$

Explanation:

We can rearrange and square both sides:
$\sqrt{8 + 7 x} = x + 2$
squaring:
$8 + 7 x = {\left(x + 2\right)}^{2}$
$8 + 7 x = {x}^{2} + 4 x + 4$
${x}^{2} - 3 x - 4 = 0$
${x}_{1 , 2} = \frac{3 \pm \sqrt{9 + 16}}{2} = \frac{3 \pm 5}{2}$
giving two solutions:
${x}_{1} = \frac{3 + 5}{2} = 4$
${x}_{2} = \frac{3 - 5}{2} = - 1$