# How do you solve x^2 + 4x + 4 = 7?

Jul 27, 2015

The solutions are:
color(green)(x=-2+sqrt(7)
color(green)( x=-2-sqrt(7)

#### Explanation:

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

${x}^{2} + 4 x - 3 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 4 , c = - 3$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

 = (4)^2-(4*1*((-3))

$= 16 + 12 = 28$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 4\right) \pm \sqrt{28}}{2 \cdot 1} = \frac{- 4 \pm 2 \sqrt{7}}{2}$

$= \frac{\cancel{2} \left(- 2 \pm \sqrt{7}\right)}{\cancel{2}}$

color(green)(x=-2+sqrt(7), x=-2-sqrt(7)