How do you solve x^2 + 10x + 25 = 0 using the quadratic formula?

May 22, 2017

$x = - 5$

Explanation:

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

Where $a {x}^{2} + b x + c = 0$.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this case, $a = 1$, $b = 10$, and $c = 25$. Now all we have to do is plug these values into the quadratic formula and simplify it.

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

$x = \frac{- 10 \pm \sqrt{{10}^{2} - 4 \left(1\right) \left(25\right)}}{2 \left(1\right)}$

$x = \frac{- 10 \pm \sqrt{100 - 100}}{2}$

$x = \frac{- 10 \pm 0}{2}$

Since adding or subtracting $0$ wouldn't change the answer at all, we actually only have a single solution instead of 2 solutions.

$x = \frac{- 10}{2} = - 5$

May 22, 2017

$y = {x}^{2} + 10 x + 25 = 0$
$D = {b}^{2} - 4 a c = 100 - 100 = 0$
$x = - \frac{b}{2 a} = - \frac{10}{2} = - 5$