How do you solve (x + 2)^2 = 13?

Mar 11, 2018

color(red)(x = -2 + sqrt13, color(blue)( -2 - sqrt13

Explanation:

${\left(x + 2\right)}^{2} = 13$

${x}^{2} + 4 x + 4 - 13 = 0$

${x}^{2} + 4 x - 9 = 0$

Standard form of quadratic equation is

$a {x}^{2} + b x + c = 0$ and it’s roots are

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

For the given equation,

$x = \frac{- 4 \pm \sqrt{{4}^{2} + \left(4 \cdot 1 \cdot 9\right)}}{2 \cdot 1}$

$x = \frac{- 4 \pm \sqrt{52}}{2} = \left(- 2 \pm \sqrt{13}\right)$

color(red)(x = -2 + sqrt13, color(blue)( -2 - sqrt13