# How do you solve (x+3)(x+5) = -7?

Oct 27, 2015

$x = - 4 \pm i \sqrt{6}$

#### Explanation:

You first need to make one side $0$.

$\left[1\right] \text{ } \left(x + 3\right) \left(x + 5\right) = - 7$

Expand $\left(x + 3\right) \left(x + 5\right)$.

$\left[2\right] \text{ } {x}^{2} + 8 x + 15 = - 7$

Add $7$ to both sides.

$\left[3\right] \text{ } {x}^{2} + 8 x + 15 + 7 = - 7 + 7$

$\left[4\right] \text{ } {x}^{2} + 8 x + 22 = 0$

Now that you have equated everything to $0$, you can solve for the roots. The roots of this quadratic equation are actually imaginary, so you should make use of the quadratic formula.

$\left[5\right] \text{ } x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\left[6\right] \text{ } x = \frac{- \left(8\right) \pm \sqrt{{\left(8\right)}^{2} - 4 \left(1\right) \left(22\right)}}{2 \left(1\right)}$

$\left[7\right] \text{ } x = \frac{- 8 \pm \sqrt{64 - 88}}{2}$

$\left[8\right] \text{ } x = \frac{- 8 \pm \sqrt{- 24}}{2}$

$\left[9\right] \text{ } x = \frac{- 8 \pm 2 i \sqrt{6}}{2}$

$\left[10\right] \text{ } \textcolor{b l u e}{x = - 4 \pm i \sqrt{6}}$