10-7 Solve Quadratic Equations with the
Quadratic Formula
Name
Date
Solve: 28x2 95x 750 0
a 28, b 95, and c 750
Identify a, b, and c.
(
(
( )(
)
)2
)
x 95 95 4 28 750
2( 28)
x
Substitute the values
a, b, and c in the
Quadratic Formula.
95 93, 025
56
Simplify
x 95 305 or x 95 305
56
56
400
or <210
56
56
50
7
or
Remember:
The Quadratic Formula
If ax2 bx c 0, where a 0,
b b2 4 ac
.
then x 2a
Write as two solutions.
Simplify.
< 15
4
Simplify.
15
The solutions of 28x2 95x 750 0 are 50
7 and < 4 .
Solve by using the Quadratic Formula. Write answers in simplest radical form.
Copyright © by William H. Sadlier, Inc. All rights reserved.
1. 6x2 + x 15
6x2 x 15 0
a 6, b 1, c 15
1 12 4 ( 6 )(15 )
x
2( 6 )
1 361
x
12
119
119
x 12 or x 12
18
20
x
or x 12
12
2. 6x2 + 7x 20
a 6, b 7, c 20
7 72 4 ( 6 )(20 )
2( 6 )
7 529
x
12
x
x
7 23
7 23
or x 12
12
{– 53, 32}
4. 6x2 5x 9 0
a 6, b 5, c 9
x
x
5 52 4 ( 6 )( 9 )
2( 6 )
5 191
12
No real solutions
3. 5x2 2x 3 0
{43, 52}
5. 2x2 15
a 2, b 0, c 15
x
02 4 ( 2 )(15 )
2( 2 )
x 120 2 30
4
4
, 30}
{ 30
2
2
Lesson 10-7, pages 264–265.
a 5, b 2, c 3
(2 )2 4 ( 5 )( 3 )
2( 5 )
2 56
x
10
No real solutions
x 2 6. 3x2 31
a 3, b 0, c 31
x
02 4 ( 3 )(31)
2( 3 )
x 372 2 93
6
6
, 93}
{ 93
3
3
Chapter 10 259
For More Practice Go To:
Solve by using the Quadratic Formula. Write answers in simplest radical form.
7. 2x2 5x 2
8. 3x2 5x 1
a 2, b 5, c 2
2
(5 ) (5 ) 4 ( 2 )(2 )
2( 2 )
5 41
x
4
(5 ) (5 ) 4 ( 3 )(1)
2( 3 )
x 5 37
6
x
x
{5 4 41, 5 4 41}
2
5 (5 ) 4 (11)( 0 )
2(11)
5 5
x 5 25 ; x 22
22
x
{5 6 37, 5 6 37}
{0, 115 }
11. 8x 2 3x2
12. 6x 3 2x2
a 3, b 8, c 2
a 21, b 4, c 0
a 2, b 6, c 3
2
2
x
a 11, b 5, c 0
a 3, b 5, c 1
2
10. 21x2 4x 0
9. 11x2 5x 0
4 ( 4 ) 4 ( 21)( 0 )
2( 4 )
4 4
x 4 16 ; x 8
8
{0, 1}
8 ( 8 ) 4 ( 3 )( 2 )
2( 3 )
x
2
6 ( 6 ) 4 ( 2 )( 3 )
2( 2 )
x 8 40 ; x 8 2 10
6
6
x
6 12
6 2 3
;x
4
4
x
{4 3
10 , 4 10
3
}
{3 2
3 , 3 3
2
}
Solve. Show all your work.
Let x width, 2x 3 length.
Solve: (2x 3)x 299; 2x2 3x 299 0
2
(3 ) (3 ) 4 ( 2 )(299 )
3 2401
;x
4
2( 2 )
23
x 3 49 ; x 13 or x .
2
4
x 13 and 2(13) 3 23; The rectangle has
a width of 13 cm and a length of 23 cm.
x
14. A bird drops a seed from 40 ft above the
ground. How many seconds does it take for
the seed to hit the ground? (Hint: d 16t 2)
Solve: 40 16t 2; 16t 2 40 0;
( )(
)
x 4 16 40 ;
(
)
2 16
x
2560
16 10
10
;x
;x
32
32
2
The seed hits the ground in
15. What are the solutions of the quadratic equation x2 4x 2?
A. x 4 B. x 2 260 Chapter 10
2 and x 4 2
2 and x 2 – 2
C. x 2 2 and x 2 2
D. no real solution
10
seconds.
2
Copyright © by William H. Sadlier, Inc. All rights reserved.
13. Geometry The area of a rectangle is 299 cm2.
The length is 3 cm less than twice the width.
What are the dimensions of the rectangle?
(Hint: A lw)