How do you solve sqrt(x - 3) + 1 = x?

Jul 25, 2015

I found:
${x}_{1} = \frac{3 + i \sqrt{7}}{2}$
${x}_{2} = \frac{3 - i \sqrt{7}}{2}$

Explanation:

I would write it as:
$\sqrt{x - 3} = x - 1$
square both sides:
$x - 3 = {\left(x - 1\right)}^{2}$ rearrange:
$x - 3 = {x}^{2} - 2 x + 1$
${x}^{2} - 3 x + 4 = 0$
Solving with the Quadratic Formula you get:
${x}_{1 , 2} = \frac{3 \pm \sqrt{9 - 16}}{2} = \frac{3 \pm \sqrt{- 7}}{2} =$
using the imaginary unit: $\sqrt{- 1} = i$ you get two solutions:
${x}_{1} = \frac{3 + i \sqrt{7}}{2}$
${x}_{2} = \frac{3 - i \sqrt{7}}{2}$