Completing the square worksheet

1. Completing the Square
Ex. x
2
+ 4x – 5 = 0
Steps:
1) Move the constant to the right side
of the equation to isolate the x’s.

2) Complete the trinomial by taking ½
of the x-value and squaring it.

3) Balance the equation by adding the new
value to the other side of the equation.

4) Simplify the equation and write the
trinomials as a single bracket squared.

5) Take the square root of each side and
solve for x to find the roots.

Ex. 3x
2
+ 12x + 16 = 0
Steps:
1) Move the constant to the right side
of the equation to isolate the x’s.

2) Common factor the x’s and write the
remaining x values in brackets.

3) Complete the trinomial by taking ½
of the x-value and squaring it.

4) Balance the equation by adding the new
value to the other side of the equation.

5) Simplify the equation and write the
trinomials as a single bracket squared.

6) Take the square root of each side and
solve for x to find the roots.