# How do you solve x^2+6=5x?

Jun 12, 2016

$x = 3$ or $x = 2$

#### Explanation:

${x}^{2} + 6 = 5 \cdot x$

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

It can be written as two factors in the form:

$\left(x + a\right) \cdot \left(x + b\right) = 0$.

Where a, b are two integers

such that :
$a + b = - 5$

and

$a \cdot b = 6$

Thus, $a = - 2$ and $b = - 3$

Substituting the values of a and b we have:

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

$\left(x - 3\right) \cdot \left(x - 2\right) = 0$

$x - 3 = 0$
Or
$x - 2 = 0$

so,
$x = 3$
or
$x = 2$