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Algebra 1

9.2.5 Practice

Algebra 19.2.5 Practice

9.2.5 Practice

9.2.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 - 5, the standard form of an equation is a x 2 + b x + c . For each expression, find the missing constant c that would make the expression a perfect square.

  1. x 2 − 6 x + c _
  1. x 2 + 2 x + c _
  1. x 2 + 14 x + c _
  1. x 2 − 4 x + c _
  1. x 2 + 24 x + c _
  1. If x 2 − 6 x + c is factored to be ( x _ _ _ _ _ ) 2 , what is the missing value of the factored form of this expression? Remember to include the sign.
  1. If x 2 + 2 x + c is factored to be ( x _ _ _ _ _ ) 2 , what is the missing value of the factored form of this expression? Remember to include the sign.
  1. If x 2 + 14 x + c is factored to be ( x _ _ _ _ _ ) 2 , what is the missing value of the factored form of this expression? Remember to enter the sign.
  1. If x 2 − 4 x + c is factored to be ( x _ _ _ _ _ ) 2 , what is the missing value of the factored form of this expression? Remember to enter the sign.
  1. If x 2 + 24 x + c is factored to be ( x _ _ _ _ _ ) 2 , what is the missing value of the factored form of this expression? Remember to enter the sign.

For each equation in questions 11 - 14, use the following scenario.

Jada looks at Mai's work and is confused. She doesn't see how Mai got her answer.

Complete Mai's missing steps by answering the questions to help Jada see how Mai solved the equation.

x 2 + 12 x = 13

Step 1 - x 2 + 12 x + _ _ _ _ _ = 13 + _ _ _ _ _

Step 2 - ( x + 6 ) 2 = 49

Step 3 - ( x + 6 ) 2 = 49

Step 4 - x + 6 = ± _ _ _ _ _

Step 5 - x + 6 = _ _ _ _ _

Step 6 - x + 6 = − _ _ _ _ _

x = 1 or x = − 13


  1. What is the missing term in Step 1?
  1. What is the missing term in Steps 4, 5, and 6?
  1. What is the value of x in Step 5?
  1. What is the value of x in Step 6?

For questions 15 - 20, solve choose the equivalent equation with a perfect square on one side.


  1. x 2 + 8 x = 2
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54
  1. x 2 + 10 x = − 13
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54
  1. x 2 − 14 x = 5
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54
  1. x 2 + 2 x = 0
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54
  1. x 2 + 4 x − 5 = 0
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54
  1. x 2 − 20 x = − 9
  1. ( x + 2 ) 2 = 9
  2. ( x + 1 ) 2 = 1
  3. ( x + 4 ) 2 = 18
  4. ( x − 10 ) 2 = 91
  5. ( x + 5 ) 2 = 12
  6. ( x − 7 ) 2 = 54

For questions 21–23, solve each equation by completing the square, then choose the two roots.


  1. x 2 − 6 x + 5 = 12
  1. x = − 1
  2. x = 5
  3. x = 2
  4. x = 7
  5. x = 6
  1. x 2 − 2 x = 8
  1. x = 9
  2. x = − 2
  3. x = 8
  4. x = 3
  5. x = 4
  1. 11 = x 2 + 4 x − 1
  1. x = 14
  2. x = 110
  3. x = − 6
  4. x = 2
  5. x = 4
  1. Solve the equation x 2 − 18 x + 60 = − 21 by completing the square.
  1. x = − 39
  2. x = 78
  3. x = 39
  4. x = 9
  5. x = − 21
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