# Question #b48d8

Sep 24, 2015

$x = 2 + i \sqrt{3} , x = 2 - i \sqrt{3}$

#### Explanation:

This quadratic expression should be solved by completing the square.

$f \left(x\right) = {x}^{2} - 4 x + 7 = 0$

Minus seven from both sides,

${x}^{2} - 4 x = - 7$

${x}^{2} - 4 x + 4 = - 3$

Write the left hand side as a square,

${\left(x - 2\right)}^{2} = - 3$

Take the square root of both sides,

$x - 2 = \pm i \sqrt{3}$

$x = 2 \pm i \sqrt{3}$
$x = 2 + i \sqrt{3} , x = 2 - i \sqrt{3}$