# How do you solve x^2-4x=10 by completing the square?

May 17, 2015

Solution is x=2$\pm \sqrt{14}$

To make a perfect square on the left side, take half the coefficient of x and then square it. Here half of -4 is -2 and its square would be 4. Now add this number on both sides of the equation. On the left side it would now be a perfect square.

${x}^{2} - 4 x + 4 = 10 + 4$

${\left(x - 2\right)}^{2} = 14$

x-2=$\pm \sqrt{14}$

x=2$\pm \sqrt{14}$