# How many solutions are there for the equation x^2 + 16 = 8x?

Apr 21, 2016

! solution only. Which is $x = 4$

#### Explanation:

Subtract $8 x$ from both sides

${x}^{2} - 8 x + 16 = 0$

Note that $\left(- 4\right) \times \left(- 4\right) = + 16 \text{ and } \left(- 4\right) + \left(- 4\right) = - 8$

So we have:

$\left(x - 4\right) \left(x - 4\right) = 0 \text{ "->" } {\left(x - 4\right)}^{2} = 0$

The only solution is $x = \left(+ 4\right)$