# How do you solve x^2=6x-25 using the quadratic formula?

Apr 18, 2017

$x = 3 + 4 i$ or $3 - 4 i$

#### Explanation:

${x}^{2} = 6 x - 25$ can be written as ${x}^{2} - 6 x + 25 = 0$

Quadratic formula gives the solution of quadratic equation $a {x}^{2} + b x + c = 0$ as

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

Hence solution of ${x}^{2} - 6 x + 25 = 0$ is

x=(-(-6)+-sqrt((-6)^2-4×1×25))/(2×1)

= $\frac{6 \pm \sqrt{36 - 100}}{2}$

= $\frac{6 \pm \sqrt{- 64}}{2}$

= $\frac{6 \pm 8 i}{2}$

= $3 \pm 4 i$

i.e. $x = 3 + 4 i$ or $3 - 4 i$