# How do you solve x^2-30=0 using the quadratic formula?

Jun 16, 2016

The quadratic formula requires us to put our quadratic into standard form:

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

${x}^{2} - 30 = 1 {x}^{2} + 0 x - 30 = 0$

Therefore

$a = 1 , \text{ " b=0 " & } c = - 30$

Then we use the quadratic formula:

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

${x}_{\pm} = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot \left(- 30\right)}}{2 \cdot 1}$

${x}_{\pm} = \pm \frac{\sqrt{120}}{2}$

we can bring the $2$ from the denominator up into the square root by first squaring it

${x}_{\pm} = \pm \sqrt{\frac{120}{4}} = \pm \sqrt{30}$

Which is the answer that we would have arrived at by just moving the $- 30$ to the right hand side and taking the square root of both sides.