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

1 Answer
Mar 20, 2016

Answer:

#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#