# How do you solve x² - 10x = 21?

Jul 1, 2015

${x}^{2} - 10 x = 21$ is a quadratic equation, so start by getting:

${x}^{2} - 10 x - 21 = 0$

Try to factor, because if it works, it's fast. But in this case, it won't factor nicely. So move on to either completing the square or

For $a {x}^{2} + b x + c = 0$, the solutions are given by:

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

So the solutions for our quadratic equation are:

$x = \frac{- \left(- 10\right) \pm \sqrt{{\left(- 10\right)}^{2} - 4 \left(1\right) \left(- 21\right)}}{2 \left(1\right)}$

$= \frac{10 \pm \sqrt{100 + 84}}{2}$

$= \frac{10 \pm \sqrt{184}}{2} = \frac{10 \pm \sqrt{4 \cdot 46}}{2}$

$= \frac{10 \pm 2 \sqrt{46}}{2} = \frac{2 \left(5 \pm \sqrt{46}\right)}{2}$

$= 5 \pm \sqrt{46}$