The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1

Teaching Notes 5.21: Solving Quadratic Equations


by Finding Square Roots


Solving quadratic equations by finding square roots involves a basic understanding of square
roots. Students may forget that positive numbers have two square roots, zero has one square root,
and negative numbers have no real square roots.


  1. Discuss the concept of squares and square roots with your students. Ask them what number
    multiplied by itself equals 9. Most students will say 3×3, which is correct. Be sure to note
    that− 3 ×−3 also equals 9. Both examples may be expressed asx^2 =9.

  2. Explain that because 9 is a positive number,x^2 =9 has two solutions. The two solutions
    arex=±



9, which meansx=3andx=−3. Emphasize that the symbol±is read ‘‘plus
or minus’’ and denotes both the positive and negative square roots.


  1. Present additional examples. Ask your students what number multiplied by itself equals 0.
    There is only one solution,x=0. Ask them what number multiplied by itself equals−49.
    There is no real solution, because no real number multiplied by itself is equal to−49. (You
    might want to mention that there are solutions for negative numbers in the imaginary
    numbers.)

  2. Review the information and example on the worksheet with your students. Note that stu-
    dents must isolate the squared term on one side of the equation before they can find the
    square root.


EXTRA HELP:
This method for solving quadratic equations by finding square roots cannot be used if there is anx
term in the equation.

ANSWER KEY:
(1)x=11 andx=− 11 (2)x=10 andx=− 10 (3)x=1andx=− 1 (4)x= 0
(5)No real solutions (6)x=7andx=− 7 (7)x= 0 (8)No real solutions
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(Challenge)Deanna rewrote the problem incorrectly. She should have subtracted 16 from
both sides of the equation and writtenx^2 =−16. When she substituted her answers in an
incorrect equation they checked. The answers would not have checked if she had substituted
them in the original equation.
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