# How do you solve x^ { 2} - 6x = 7?

May 2, 2018

$x = 7 \mathmr{and} x = \left(- 1\right)$

#### Explanation:

Subtract 7 from both sides.
$\implies {x}^{2} - 6 x - 7 = 0$
We need to factorize this expression by splitting its middle term.

$\implies {x}^{2} - 7 x + x - 7 = 0$
$\implies x \left(x - 7\right) + 1 \left(x - 7\right) = 0$
$\implies \left(x - 7\right) \left(x + 1\right) = 0$

$\implies x - 7 = 0 \mathmr{and} x + 1 = 0$
$\implies x = 7 \mathmr{and} x = \left(- 1\right)$

May 2, 2018

$x = 7$
$x = - 1$

#### Explanation:

${x}^{2} - 6 x = 7$ Subtract $7$ from both sides:
${x}^{2} - 6 x - 7 = 0$
$- 7 , 1$ are factors of $- 7$ that add up to $6$, so they will be factors:
$\left(x - 7\right) \left(x + 1\right) = 0$ Using the $0$ product property:
$x - 7 = 0$
$x = 7$
and
$x + 1 = 0$
$x = - 1$