# How do you solve the equation x^2-8x+15=0 by completing the square?

Nov 15, 2016

x= 5, 3

#### Explanation:

To make a complete square of the terms ${x}^{2}$ and 8x add and subtract 16 in the given expression as shown below:

${x}^{2} - 8 x + 16 - 16 + 15$.

To arrive at the number to be added and subtracted, first half the coefficient of x, then square that figure to get the required number. It has to be made sure that coefficient of ${x}^{2}$ in this exercise is 1

As can be seen now, the terms ${x}^{2} - 8 x + 16$ are equivalent of ${\left(x - 4\right)}^{2}$. Now we can solve the given equation,

${\left(x - 4\right)}^{2} - 1 = 0$

${\left(x - 4\right)}^{2} = 1$

x-4=$\pm$1

Therefore, x=5 , 3