How do you solve x^2 + 6x = 3 using completing the square?

Jul 23, 2015

To complete the square you add $9$ to both sides.

Explanation:

Method : you halve the $x$-coefficient ($6$) to get $3$, and the square of that ($9$) is needed to complete the square.

$\to {x}^{2} + 6 x + 9 = 3 + 9$

$\to {\left(x + 3\right)}^{2} = 12 \to x + 3 = \pm \sqrt{12} = \pm 2 \sqrt{3}$

$\to {x}_{1 , 2} = - 3 \pm 2 \sqrt{3}$

(remember $\pm$ means two solutions, one with + and one with -)