# How do you solve 92- 42x = 2x^2?

May 2, 2018

$x = 2 \mathmr{and} x = - 23$

#### Explanation:

Notice that it is a quadratic equation because there is an ${x}^{2}$ term. The first step is to move all the terms to one side to make the equation equal to $0$

$2 {x}^{2} + 42 x - 92 = 0 \text{ } \leftarrow \div 2$

${x}^{2} + 21 x - 46 = 0 \text{ } \leftarrow$ find factors if possible

$\left(x + 23\right) \left(x - 2\right) = 0$

Either factor could be equal to $0$

$x + 23 = 0 \text{ } \rightarrow x = - 23$

$x - 2 = 0 \text{ } \rightarrow x = 2$