# How do you solve using the completing the square method x^2 - 30x = -125?

Mar 20, 2016

$x = 5 \mathmr{and} x = 25$

#### Explanation:

One usually starts by dividing throughout by the coefficient of ${x}^{2}$ and taking all $x$ terms to one side. The given equation is already in this format.

Next step, take the coefficient of $x$, half it, square it, and add it to both sides.

$\therefore {x}^{2} - 30 x + {\left(- \frac{30}{2}\right)}^{2} = - 125 + {\left(- \frac{30}{2}\right)}^{2}$

Now write the left hand side as a perfect square and simplify the right hand side.

$\therefore {\left(x - 15\right)}^{2} = - 125 + \frac{900}{4} = 100$

Now take the square root on both sides and solve for $x$

$\therefore x - 15 = \pm \sqrt{100} = \pm 10$

$\therefore x = 15 \pm 10$

$= 25 \mathmr{and} 5$