Name
Class
Date
Reteaching 5-7
Completing the Square
OBJECTIVE: Solving quadratic equations by
completing the square
MATERIALS: None
Perfect square trinomials are equations in the form x2 + 2kx + k2,
which can be factored into (x + k)2. Completing the square produces a
perfect square trinomial.
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To complete the square, you must write the equation so that the
coefficient of the x2 term equals 1.
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Example
Complete the square to solve the quadratic equation.
2x2 + 20x - 22 = 0
2x2 + 20x - 22 = 0
Look to see whether the x2 coefficient is 1.
x2 + 10x - 11 = 0
Divide each side by 2 to eliminate the x2 coefficient.
x2 + 10 x - 11 = 0
Circle the coefficient of the linear term.
x2 + 10 x = 11
x2 + 10 x + 25 = 11 + 25
Divide the circled number by 2, square it, and add
the result to each side.
(x + 5)2 = 36
Factor the perfect square trinomial.
x + 5 = 46
Take the square root of each side.
x = -5 4 6
Solve for x.
x = 1 and -11
Simplify.
Exercises
Solve each equation by completing the square.
1. x2 + 4x = 21
2. x2 - 8x = 33
3. x2 + 10x = -5
4. 3x2 + 10x + 3 = 0
5. 3x2 + 4x = 3
6. x2 - 5x - 5 = 0
7. x2 + 7x = 0
8. 2x2 - 7x - 4 = 0
9. x2 - x - 7 = 0
10. x2 - 8x + 4 = 0
11. x2 - 6x + 6 = 0
12. x2 + 2x = 15
13. x2 + 2x - 5 = 0
14. 2x2 + 8x - 10 = 0
15. 4x2 + 4x = 3
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Lesson 5-7 Reteaching
Algebra 2 Chapter 5
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Add 11 to each side to get the variables on one side
of the equal sign.