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9-4 Solving Quadratic Equations by Completing the Square
Find the value of c that makes each trinomial a perfect square.
2
1. x − 18x + c
SOLUTION: In this trinomial, b = –18.
So, c must be 81 to make the trinomial a perfect square.
2
2. x + 22x + c
SOLUTION: In this trinomial, b = 22.
So, c must be 121 to make the trinomial a perfect square.
2
3. x + 9x + c
SOLUTION: In this trinomial, b = 9.
So, c must be
to make the trinomial a perfect square.
2
4. x − 7x + c
SOLUTION: In this trinomial, b = –7.
eSolutions
Powered
by Cognero
So, cManual
must -be
to make the trinomial a perfect square.
Solve each equation by completing the square. Round to the nearest tenth if necessary.
Page 1
9-4 Solving
Quadratic
Equations by Completing the Square
So, c must
be
to make the trinomial a perfect square.
2
4. x − 7x + c
SOLUTION: In this trinomial, b = –7.
So, c must be
to make the trinomial a perfect square.
Solve each equation by completing the square. Round to the nearest tenth if necessary.
2
5. x + 4x = 6
SOLUTION: The solutions are about –5.2 and 1.2.
2
6. x − 8x = −9
SOLUTION: The solutions are about 1.4 and 6.6.
Find the value of c that makes each trinomial a perfect square.
2
24x + -cPowered by Cognero
11. x −Manual
eSolutions
SOLUTION: In this trinomial, b = –24.
Page 2
9-4 Solving Quadratic Equations by Completing the Square
The solutions are about 1.4 and 6.6.
Find the value of c that makes each trinomial a perfect square.
2
11. x − 24x + c
SOLUTION: In this trinomial, b = –24.
So, c must be 144 to make the trinomial a perfect square.
2
13. x + 17x + c
SOLUTION: In this trinomial, b = 17.
So, c must be
to make the trinomial a perfect square.
2
15. x − 13x + c
SOLUTION: In this trinomial, b = –13.
So, c must be
to make the trinomial a perfect square.
2
17. x − 15x + c
SOLUTION: In this trinomial, b = –15.
eSolutions
Powered to make the trinomial a perfect square.
by Cognero
So, cManual
must -be
Solve each equation by completing the square. Round to the nearest tenth if necessary.
Page 3
9-4 Solving
Quadratic
Equations by Completing the Square
So, c must
be
to make the trinomial a perfect square.
2
17. x − 15x + c
SOLUTION: In this trinomial, b = –15.
So, c must be
to make the trinomial a perfect square.
Solve each equation by completing the square. Round to the nearest tenth if necessary.
2
19. x + 6x − 16 = 0
SOLUTION: The solutions are –8 and 2.
2
21. x − 8x − 1 = 8
SOLUTION: The Manual
solutions
are –1byand
9.
eSolutions
- Powered
Cognero
2
23. x − 11x + 3 = 5
Page 4
9-4 Solving
Quadratic
by Completing the Square
The solutions
are –8Equations
and 2.
2
21. x − 8x − 1 = 8
SOLUTION: The solutions are –1 and 9.
2
23. x − 11x + 3 = 5
SOLUTION: The solutions are about –0.2 and 11.2.
eSolutions Manual - Powered by Cognero
Page 5
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