Download Solving Quadratics using Bust the “b” ax + bx + c = 0

Solving Quadratics using Bust the “b”
ax2 + bx + c = 0
STEPS:
1.
Factor out the GCF if necessary.
2.
Make sure that a is positive.
(if not divide through by –1)
3.
Open two parenthesis with ax
(ax
)(ax
)
*you now have a “fudge (extra) factor” of a
4.
Multiply the first and the last numbers.
Find factors of ac that combine to = b.
5.
Look inside each parenthesis for GCFs
6.
Solve
NOTE: If Bust the “b” fails to yield solutions, there are no rational roots you
must complete the square or use the quadratic formula.
Example:
2x2 + 7x – 15 =0
(2x )(2x
)
*fudge = 2
2*15 = 30
1
30
2
15
3
10
5
6
(2x + 10)(2x – 3) =0
2(x + 5)(2x – 3) =0
x + 5 = 0 or 2x - 3 = 0
x = -5 or x = 3/2
Example: 6x2 - 19x + 10
(6x )(6x
)=0
*fudge = 6
6*10 = 60
1
2
3
4
5
6
(6x - 4)(6x – 15) = 0
2(3x - 2)3(2x – 5) = 0
x=
2
5
, x=
2
3
Try: 4x2 – 4x –15 = 0
Try: 10x2 – 34x + 12 = 0
Try: 3a4 + a2 = 18
60
30
20
15
12
10