Question

How do you solve the equation $x^2-16x=-20$ by completing the square?

Answer 1

Find the equation $x^2-16x=-20$ by completing the square:

Completing the square means the equation should be in $a{x}^2+bx+c$:

$\begin{array}{rcl}{x}^2-16x& =& -20\\ & \Rightarrow & x^2-16x+8^2-8^2=-20\\ & \Rightarrow & {\left(x-8\right)}^2-64=-20\\ & \Rightarrow & {\left(x-8\right)}^2=44\\ & \Rightarrow & x-8=\pm \sqrt{44}\\ & \Rightarrow & x=8\pm 2\sqrt{11}\\ & \Rightarrow & x=8\pm 2\sqrt{11}\end{array}$

Hence, the equation after using the completing the square method is $\begin{array}{rcl}x& =& 8\pm 2\sqrt{11}\end{array}$.