# How do you solve x^2 -5x= -7 using the quadratic formula?

May 16, 2017

Add $7$ to both sides of the equation to make it equal to $0$:

${x}^{2} - 5 x + 7 = 0$

Then use the quadratic formula and plug in the values:

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

$x = \frac{5 \pm \sqrt{25 - 4 \left(1\right) \left(7\right)}}{2 \left(1\right)} = \frac{5 \pm \sqrt{- 3}}{2}$

If you've learned about complex numbers, this can be simplified to

$x = \frac{5}{2} \pm \frac{i \sqrt{3}}{2}$