Solved Examples and Worksheet for Solving Quadratic Equations by Finding Square Roots

Q1Solve the equation k24 = 0.

A. k = 0,2
B. k = 0,1
C. k = 0
D. k = 1

Solutions
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Step: 1
k24 = 0
  [Original equation.]
Step: 2
k2 = 0
  [Multiply each side with 4.]
Step: 3
k = 0
  [Evaluate square root on both sides.]
Correct Answer is :   k = 0
Q2Solve 10q2 - 35 = 15 and round its result to its nearest hundredth.

A. ±2.02
B. ±3.23
C. ±2.24
D. ±2.46

Solutions
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Step: 1
10q2 - 35 = 15
  [Original equation.]
Step: 2
10q2 = 50
  [Add 35 to each side.]
Step: 3
q2 = 5
  [Divide each side by 10.]
Step: 4
q = ±√5
  [Evaluate square root on both sides.]
Step: 5
q = ±2.23
  [Round to the nearest hundredth.]
Correct Answer is :   ±2.24
Q3What is the value of x, if 2x2 - 3 = 159?
A. 9
B. ± 9
C. 81
D. 8

Solutions
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Step: 1
2x2 - 3 = 159
  [Original equation.]
Step: 2
2x2 - 3 + 3 = 159 + 3
  [Add 3 to both sides.]
Step: 3
2x2 = 162
  [Simplify each side.]
Step: 4
x2 = 81
  [Divide each side by 2.]
Step: 5
x = 81
  [Find the square roots.]
Step: 6
x = ± 9
  [Since 92 = 81 and (-9)2 = 81.]
Step: 7
The value of x, if 2x2 - 3 = 159, is ± 9.
Correct Answer is :   ± 9
Q4What is the value of x, if - 7x2 = - 35?
A. ± 5
B. ± 2
C. ± 6
D. ± 7

Solutions
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Step: 1
- 7x2 = - 35
  [Original equation.]
Step: 2
- 7x2 × - 1 = - 35 × - 1
  [Multiply each side by - 1.]
Step: 3
7x2 = 35
  [Simplify.]
Step: 4
x2 = 5
  [Divide each side by 7.]
Step: 5
x = ± 5
  [Find the square roots.]
Step: 6
The value of x is ± 5.
Correct Answer is :   ± 5
Q5What is the value of x, if 4x2 - 32 = 32?
A. ± 6
B. ± 4
C. ± 7
D. ± 5

Solutions
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Step: 1
4x2 - 32 = 32
  [Original equation.]
Step: 2
4x2 - 32 + 32 = 32 + 32
  [Add 32 to both sides.]
Step: 3
4x2 = 64
  [Simplify.]
Step: 4
x2 = 16
  [Divide by 4 on both sides.]
Step: 5
x = ± 4
  [Find the square roots.]
Correct Answer is :   ± 4
Q6What is the value of x, if x2 = 45?

A. ± 65
B. ± 55
C. ± 45
D. ± 35

Solutions
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Step: 1
x2 = 45
  [Original equation.]
Step: 2
x = ± 45
  [Find the square roots.]
Step: 3
x = ± 9 × 5
  [Write as square factors.]
Step: 4
x = ± 35
  [Simplify.]
Correct Answer is :   ± 35
Q7Find the value of x, if 9x2 = 225.

A. ± 5
B. ± 6
C. ± 8
D. ± 7

Solutions
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Step: 1
9x2 = 225
  [Original equation.]
Step: 2
9x29 = 2259
  [Divide each side by 9.]
Step: 3
x2 = 25
  [Simplify.]
Step: 4
x = ± 25
  [Find square roots.]
Step: 5
x = ± 5
  [Evaluate square root.]
Correct Answer is :   ± 5
Q8The largest pizza ever made in a pizza center had an area of 530.66 square inches. What was the radius of the pizza, if its area is given by the equation A = 3.14r2, where A is its area in square inches and r is its radius in inches?

A. 13.5
B. 13
C. 14
D. 12.5

Solutions
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Step: 1
A = 3.14r2
  [Original equation.]
Step: 2
530.66 = 3.14r2
  [Substitute the values.]
Step: 3
530.663.14 = 3.14r 23.14
  [Divide each side by 3.14]
Step: 4
169 = r2
  [Simplify.]
Step: 5
r = 169
  [Apply square root to both sides.]
Step: 6
r = ± 13
  [Evaluate the square root on each side.]
Step: 7
r = 13
  [Radius is always a positive value.]
Step: 8
So, the radius of the pizza is 13 inches.
Correct Answer is :   13

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