# How do you solve 4p^2=-25p-25 using the quadratic formula?

Apr 11, 2018

$- 5 \mathmr{and} \frac{- 5}{4}$

#### Explanation:

To use the quadratic formula our function has to be in the form:

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

So, let's start off by subtracting $4 {p}^{2}$ from both sides, to get it into that form. That gives us:

$0 = - 4 {p}^{2} - 25 p - 25$

I'm also going to multiply both sides by $- 1$, to eliminate all of the negatives. You don't have to do this, but it will make the process quite a bit cleaner. That leaves us with:

$0 = 4 {p}^{2} + 25 p + 25$

So, $a = 4$, $b = 25$, $c = 25$

Now we simply substitute our values into the quadratic equation

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

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

= $\frac{- 25 \pm \sqrt{225}}{8}$

= $\frac{- 25 \pm 15}{8}$

= $\frac{- 40}{8} \mathmr{and} \frac{- 10}{8}$

= $- 5 \mathmr{and} \frac{- 5}{4}$