# How do you solve x^2 + 5x + 3 = 9?

Jul 2, 2018

$x = - 6 , x = 1$

#### Explanation:

Given: ${x}^{2} + 5 x + 3 = 9$

Solve means to find the values of $x$ that make the equation true.

Put the equation in the form: $A {x}^{2} + B x + C = 0$ by subtraction $9$ from both sides of the equation:

${x}^{2} + 5 x - 6 = 0$

Factor the equation by finding two numbers that multiply to

$\underline{A \cdot C = - 6 \text{ and sum to } B = 5}$
$- 2 \cdot 3 = - 6 \text{ "-2+3 = 1" doesn't work}$
$- 6 \cdot 1 = - 6 \text{ "-6 + 1 = -5" doesn't work}$
$6 \cdot - 1 = - 6 \text{ " 6 + -1 = 5" works}$

${x}^{2} + 5 x - 6 = 0 \implies \text{ } \left(x + 6\right) \left(x - 1\right) = 0$

x + 6 = 0; " " x - 1 = 0

$x = - 6 , x = 1$