What number that needs to be added to both sides of the equation #x^2 + 4x = 96# to complete the square?

1 Answer
Dec 15, 2015

Answer:

The number to be added to both sides is 4.

Explanation:

Divide the coefficient of the #x# term by #2#, then square the result. This number will be added to both sides of the equation. For the quadratic equation #x^2+4x=96#, the coefficient of the #x# term is #4#. So #(4/2)^2=4#.

#x^2+4x+4=96+4#

#x^2+4x+4=100#

#(x+2)^2=100#

Take the square root of both sides.

#x+2=+-10#

Subtract #2# from both sides.

#x=-2+-10#

Solve for #x#.

#x=-2+10=8#

#x=-2-10=-12#

#x=8, -12#