How do you solve x^2+8x=20 using completing the square?

Jun 19, 2018

${\left(x + 4\right)}^{2} - 16 = 20$

${\left(x + 4\right)}^{2} = 36$

Square root both sides

$x + 4 = \setminus \pm 6$

$x + 4 = 6 \mathmr{and} x + 4 = - 6$

$x = 2 \mathmr{and} x = - 10$

Jun 19, 2018

$x = 2$ and $x = - 10$

Explanation:

When we complete the square, we want to take half of our $b$ value, square it, and add it to the left side. Doing this, we get

${x}^{2} + 8 x + \textcolor{b l u e}{16} = 20 + \textcolor{b l u e}{16}$

$16$ is the value ${\left(\frac{8}{2}\right)}^{2}$. Notice, we add it to both sides to maintain the equality.

Our equation can be further simplified as

${\left(x + 4\right)}^{2} = 36$

Taking the square root of both sides, we get

$x + 4 = 6$ and $x + 4 = - 6$

Solving these equations gives us

$x = 2$ and $x = - 10$

Hope this helps!