# How do you find the zeros of x^2= 30-13x?

Jan 7, 2017

First, get all of the terms for the quadratic on the left side of the equation, factor the quadratic and then solve each term for $0$. See full explanation below.

#### Explanation:

First, get all terms on the left side of the equation while keeping the equation balanced:

${x}^{2} + \textcolor{red}{13 x} - \textcolor{b l u e}{30} = 30 - 13 x + \textcolor{red}{13 x} - \textcolor{b l u e}{30}$

${x}^{2} + \textcolor{red}{13 x} - \textcolor{b l u e}{30} = 30 - \textcolor{b l u e}{30} - 13 x + \textcolor{red}{13 x}$

${x}^{2} + \textcolor{red}{13 x} - \textcolor{b l u e}{30} = 0 - 0$

${x}^{2} + \textcolor{red}{13 x} - \textcolor{b l u e}{30} = 0$

We can now factor the quadratic:

$\left(x + 15\right) \left(x - 2\right) = 0$

Finally we can solve each term for $0$:

Solution 1)

$x + 15 = 0$

$x + 15 - \textcolor{red}{15} = 0 - \textcolor{red}{15}$

$x + 0 = - 15$

$x = - 15$

Solution 2)

$x - 2 = 0$

$x - 2 + \textcolor{red}{2} = 0 + \textcolor{red}{2}$

$x - 0 = 2$

$x = 2$