Question

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

Answer 1

`x=5 or 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^2-30x+(-30/2)^2=-125+(-30/2)^2`

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

`therefore (x-15)^2=-125+900/4=100`

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

`therefore x-15=+-sqrt100=+-10`

`therefore x=15+-10`

`=25 or 5`