# How do you factor -4/3x+4/9=-x^2?

Aug 15, 2017

x^2-4/3x+4/9=color(blue)((x-2/3)^2

Refer to the explanation for the process.

#### Explanation:

Factor:

$- \frac{4}{3} x + \frac{4}{9} = - {x}^{2}$

Add ${x}^{2}$ to both sides.

${x}^{2} - \frac{4}{3} x + \frac{4}{9} = 0$

Since the desired answer is the factors of the equation, the $0$ will not be included in the expression.

Find two numbers that when added equal $- \frac{4}{3}$ and when multiplied equal $\frac{4}{9}$. Both requirements are met by $- \frac{2}{3}$.

${x}^{2} - \frac{4}{3} x + \frac{4}{9} = \left(x - \frac{2}{3}\right) \left(x - \frac{2}{3}\right)$

${x}^{2} - \frac{4}{3} x + \frac{4}{9} = {\left(x - \frac{2}{3}\right)}^{2}$