# How do you solve using the quadratic formula x^2-25=0?

May 7, 2015

If you really must use the quadratic formula,
we need to express our equation in the form:
$a {x}^{2} + b x + c = 0$

${x}^{2} - 25 = 0$
becomes
$\left(1\right) {x}^{2} + \left(0\right) x + \left(- 25\right) = 0$

The quadratic formula tells us the solution(s) is/are
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
or, for our example
$x = \frac{0 \pm \sqrt{{0}^{2} - 4 \left(1\right) \left(- 25\right)}}{2 \left(1\right)}$

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

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

$x = \pm 5$