1. Algebra
12.4
Completing the Square

2. Solve: x² + 10x - 24 = 0 (x + 12)(x - 2) = 0 -12, 2 -12, 2
The 3 Methods of Solving a Quadratic Equation in the form ax²+ bx + c = 0
Solve: x² + 10x - 24 = 0
1. Factoring
(x + 12)(x - 2) = 0
-12, 2
2. Quadratic Formula
-12, 2
3. Completing the Square
We learn today

3. Solve x² + 10x - 24 = 0 by Completing the Square
Move constant to right and leave a space
x² + 10x = 24
+25
+25
Take ½ of b and square it.
Add result to both sides.
(x + 5
)² = 49
Simplify both sides
(left side is a PST)
x + 5 = ± √49
Take square root of both sides
x = -5 ± 7
Isolate x to solve
-12, 2

4. STEPS Completing the Square: 1.Write equation as ax²+ bx (space) = c
2. Add
to both sides
3. Write left side as PST and simplify right side
4. Take the square root of both sides
5. Isolate x to solve

5. Warm-Up: What would you add to “complete the square?”
Expression 10
100
x²+ 20x 16 -4
x²- 8x
x²+ 5x
Take ½ the
numerator
Double the
denominator

6. Try it together: x²- 8x + 12 = 0
Move constant to right and leave a space
x² - 8x = -12
+16
+16
Take ½ of b and square it.
Add result to both sides.
(x - 4
)² = 4
Simplify both sides
(left side is a PST)
x - 4 = ± √4
Take square root of both sides
x = 4 ± 2
Isolate x to solve
6, 2

7. Try it together: x²- 6x - 11 = 0
Move constant to right and leave a space
x² - 6x = 11
+ 9 +9
Take ½ of b and square it.
Add result to both sides.
(x - 3
)² = 20
Simplify both sides
(left side is a PST)
x – 3 = ±
√20
Take square root of both sides
x = 3 ±
2√5
Isolate x to solve

8. Try it together: x²- 2/3x - 3 = 0
Move constant to right and leave a space
x² - 2/3x = 3
+1/9
+1/9
Take ½ of b and square it.
Add result to both sides.
(x -
1/3
)² = 28/9
Simplify both sides
(left side is a PST)
x – 1/3 = ±
Take square root of both sides
x = ±
Isolate x to solve
Simplify over one
denominator

9. Homework
pg # 3-37 odd
Skip #13 and 15
Let’s Look at #17