Download Algebra 2 5.5 Completing the Square Name: Essential Question

Algebra 2
5.5 Completing the Square
Name: _______________________
Essential Question: How do we solve quadratic equations by using the square root property and by completing
the square?
Warm Up: Factor each of the following.
a. x2 + 16x + 64
b. x2 – 34x + 289
c. 4x2 – 12x + 9
Vocabulary: ________________________________ is the process of manipulating an equation so that one
side of the equation contains a perfect square trinomial. To complete the square on x2 + bx, add (1/2b)2
to both sides of the equation. x2 + bx + (1/2b)2 = (x + 1/2b)2 = (x + b/2)2
Solving using the Square Root Property:
a. x2 + 14x + 49 = 64
b. x2 – 4x + 4 = 13
How to complete the square: Use x2 + 2x – 8 = 0
First step, get everything without an x on the other side of the equation.
Second step, find b so that we can see what 12 b is.
Third step, complete the perfect square trinomial. (Remember that whatever you do to one side of the
equation, you must also do to the other side)
We now have a perfect square trinomial, which can be factored into a binomial square. (Remember we just
found the perfect square trinomial by expanding the binomial square. By factoring we are just “un-multiplying”
it.)
Fourth step, factor the perfect square trinomial.
Examples:
1. Find the value for c that makes x2 + 12x + c a perfect square. Then write the trinomial as a perfect
square.
2. Solve by completing the square.
a. x2 + 4x – 12 = 0
b. 3x2 – 2x – 1 = 0
Summarizer: Complete the square for 0 = x2 - 10x + 10.
c. x2 + 4x + 11 = 0