AnswersCommon Core Algebra I 2014 - MA3109 B-CRSolving Quadratic Equations: Completing the Square

Solving Quadratic Equations: Completing the Square Answers

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1
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Which are the solutions of x2 = 19x + 1?

A
StartFraction 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 19 EndRoot Over 2 EndFraction
Option A
B
StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction
Option B
C
StartFraction negative 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 19 EndRoot Over 2 EndFraction
Option C
D
StartFraction negative 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 365 EndRoot Over 2 EndFraction
Option D
2
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Solve x2 + 14x = −24 by completing the square.What is the solution set of the equation?

A
{−12, −2}
B
{−7, 7}
C
{−6, −4}
D
{−5, 5}
3

Which are the solutions of the quadratic equation?x2 = 9x + 6

A
StartFraction negative 9 minus StartRoot 105 EndRoot Over 2 EndFraction comma StartFraction negative 9 + StartRoot 105 EndRoot Over 2 EndFraction
Option A
B
StartFraction negative 9 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFraction negative 9 + StartRoot 57 EndRoot Over 2 EndFraction
Option B
C
StartFraction 9 minus StartRoot 105 EndRoot Over 2 EndFraction comma StartFraction 9 + StartRoot 105 EndRoot Over 2 EndFraction
Option C
D
StartFraction 9 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFraction 9 + StartRoot 57 EndRoot Over 2 EndFraction
Option D
4

What value of c makes x2 − 12x + c a perfect square trinomial?

A
−36
B
−24
C
24
D
36
5

What number should be added to both sides of the equation to complete the square?x2 + 3x = 6

A
Option
Option A
B
(StartFraction 3 Over 2 EndFraction) squared
Option B
C
3
D
62
6

Which are the solutions of the quadratic equation?x2 = –5x – 3

A
–5, 0
B
StartFraction negative 5 minus StartRoot 13 EndRoot Over 2 EndFraction comma StartFraction negative 5 + StartRoot 13 EndRoot Over 2 EndFraction
Option B
C
StartFraction 5 minus StartRoot 13 EndRoot Over 2 EndFraction comma StartFraction 5 + StartRoot 13 EndRoot Over 2 EndFraction
Option C
D
5, 0
7

Bao Yu is completing the square to solve the polynomial equation.x2 – x – 3 = 0

A
adding –x to both sides of the equation
B
adding –3 to both sides of the equation
C
isolating the first term, x2
D
isolating the constant, –3
8

What value of c makes x2 + 6x + c a perfect square trinomial?

A
3
B
6
C
9
D
12
9

Which are the solutions of the quadratic equation?x2 = 7x + 4

Question illustration
A
Option
Option A
–
–7, 0
C
Option
Option C
7
7, 0
10

What value of c makes x2 − 24x + c a perfect square trinomial?

A
−144
B
−48
C
48
D
144
11

Which are the solutions of x2 = –11x + 4?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Which are the solutions of x2 = 19x + 1?

A
StartFraction 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 19 EndRoot Over 2 EndFraction
Option A
B
StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction
Option B
C
StartFraction negative 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 19 EndRoot Over 2 EndFraction
Option C
D
StartFraction negative 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 365 EndRoot Over 2 EndFraction
Option D
13

Which are the solutions of x2 = –5x + 8?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

What value of c makes x2 − 12x + c a perfect square trinomial?

A
−36
B
−24
C
24
D
36
15

Which are the solutions of x2 = –13x – 4?

Question illustration
0
0, 13
0
0, –13
C
Option
Option C
D
Option
Option D
16

Solve x2 + 14x = −24 by completing the square.What is the solution set of the equation?

{
{−12, −2}
{
{−7, 7}
{
{−6, −4}
{
{−5, 5}
17

What value of c makes x2 − 24x + c a perfect square trinomial?

−
−144
−
−48
4
48
1
144
18

What number should be added to both sides of the equation to complete the square?x2 + 3x = 6

Question illustration
A
Option
Option A
B
Option
Option B
3
3
6
62
19

Bao Yu is completing the square to solve the polynomial equation.x2 – x – 3 = 0

a
adding –x to both sides of the equation
a
adding –3 to both sides of the equation
i
isolating the first term, x2
i
isolating the constant, –3
20

What number should be added to both sides of the equation to complete the square?x2 + 8x = 4

4
4
8
8
1
16
3
32

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