# How do you solve (x - 4)(x + 5) = 7 using the quadratic formula?

Feb 20, 2016

$x = \frac{- 1 \pm \sqrt{109}}{2}$

#### Explanation:

1. Simplify the equation by FOIL METHOD
$\left(x - 4\right) \left(x + 5\right) = 7$
${x}^{2} + 5 x - 4 x - 20 = 7$
#x^2+x-27=0
2. Identify the values for a, b, and c
$a = 1$
$b = 1$
$c = - 27$
3. Use the standard formula, which is
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
4. Plug in the values
$x = \frac{- 1 \pm \sqrt{{1}^{2} - 4 \left(1\right) \left(- 27\right)}}{2 \left(1\right)}$
$x = \frac{- 1 \pm \sqrt{1 + 108}}{2}$
$x = \frac{- 1 \pm \sqrt{109}}{2}$
$x = \frac{- 1 \pm \sqrt{109}}{2}$