# How do you solve (x – 2) ² = 4(4 – x)?

Mar 27, 2016

$x = - 2 \sqrt{3}$ or $x = 2 \sqrt{3}$

#### Explanation:

Simplifying ${\left(x - 2\right)}^{2} = 4 \left(4 - x\right)$, we get

${x}^{2} - 4 x + 4 = 16 - 4 x$ or

${x}^{2} - 4 x + 4 x + 4 - 16 = 0$ or

${x}^{2} - 12 = 0$ or

$\left(x + \sqrt{12}\right) \left(x - \sqrt{12}\right) = 0$ or

$x = - \sqrt{12} = - 2 \sqrt{3}$ or $x = 2 \sqrt{3}$