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Algebra II/Trig
Unit 4 Day 5 – Completing the Square
In order to solve a quadratic, you need to be able to manipulate different forms of an equation to get it into the best possible
form for solving. Taking the square root of both sides is an easy method, but you can only do this you do not have a “bx” term
or when you have a perfect square trinomial.
How to solve with the Square Root Property:
1. x2 + 6x + 9 = 36
A.
B.
C.
D.
E.
F.
Factor the left hand side of the equation.
Take the square root of both sides.
Make sure you write ± in front of the radical.
Simplify the radical.
Get the variable by itself.
If there are no radical or imaginary parts in the solution, find
the two exact answers. If there are radical or imaginary parts
in the answer, then do part G.
G. Write your answer in simplified radical form, unless a decimal
answer is asked for OR you are doing a word problem where
a decimal makes more sense.
How to Complete the Square when a = 1:
2. x2 - 10x + 25 = 27
3. x2 – 2x – 2 = 0
A. If the equation is in standard form (ax2 + bx + c), where a = 1,
move the constant (c) to the other side of the problem.
B. Create a perfect square trinomial: take half of (b), square it,
and add it to both sides.
C. Factor the perfect square trinomial and simplify the
constants.
D. Take the square root of both sides so that you can solve the
equation.
4. x2 – 14x + 1 = 0
How to Complete the Square when a ≠ 1:
5. 2x2 – 4x – 10 = 0
A. If the equation is in standard form (ax2 + bx + c), where a ≠ 1,
move the constant (c) to the other side of the problem.
B. Divide both sides of the problem by the coefficient of x2 (a)
C. Create a perfect square trinomial: take half of (b), square it,
and add it to both sides.
D. Factor the perfect square trinomial and simplify the
constants.
E. Take the square root of both sides so that you can solve the
equation.
6. 10 – 8x = 5x2 + 2x + 3
Practice: REMEMBER TO CHECK TO SEE IF YOU ALREADY HAVE A PERFECT SQUARE TRINOMIAL!!!
1. x2 – 6x + 9 = 25
2. x2 + 4x – 12 = 0
3. x2 – 6x + 7 = 0
4. x2 – 10x + 2 = 3
5. 2x2 + 8x – 12 = 6
6. x2 + 3x – 5 = 0
7. 2x2 + 5x – 9 = 0
8. 3x2 + 5x + 12 = 10