Solve using the quadratic formula
This lesson shows how to solve using the quadratic formula. To use the quadratic formula, you need to identify a, b, and c using the standard form of a quadratic equation.
You can also write the quadratic formula as x = [-b ± √(b
2 - 4ac)]/2a
How to identify a, b, and c
The standard form is ax
2 + bx + c = 0
1) for 6x
2 + 8x + 7 = 0, we get a = 6, b = 8, and c = 7
2) for x
2 + 8x - 7 = 0, we get a = 1, b = 8, and c = -7
2) for -x
2 - 8x + 7 = 0, we get a = -1, b = -8, and c = 7
More examples showing how to solve using the quadratic formula
Example #1:
Solve using the quadratic formula x
2 + 8x + 7 = 0
a = 1, b = 8, and c = 7
x = [-b ± √(b
2 - 4ac))] / 2a
x = [-8 ± √(8
2 - 4 × 1 × 7)] / 2 × 1
x = [-8 ± √(64 - 4 × 1 × 7)] / 2
x = [-8 ± √(64 - 4 × 7)] / 2
x = [-8 ± √(64 - 28)] / 2
x = [-8 ± √(36)] / 2
x = (-8 ± 6 ) / 2
x
1 = (-8 + 6 ) / 2
x
1 = (-2 ) / 2
x
1 = -1
x
2 = (-8 - 6 ) / 2
x
2 = (-14 ) / 2
x
2 = -7
Example #2:
Solve using the quadratic formula 4x
2 - 11x - 3 = 0
a = 4, b = -11, and c = -3
x = [-b ± √(b
2 - 4ac)] / 2a
x = [- -11 ± √( (-11)
2 - 4 × 4 × -3)] / 2 × 4
x = [11 ± √(121 - 4 × 4 × -3)] / 8
x = [11 ± √(121 - 4 × -12)] / 8
x = [11 ± √(121 + 48)] / 8
x = [11 ± √(169)] / 8
x = (11 ± 13 ) / 8
x
1 = (11 + 13 ) / 8
x
1 = (24 ) / 8
x
1 = 3
x
2 = (11 - 13 ) / 8
x
2 = (-2 ) / 8
x
2 = -1/4
Example #3:
Solve using the quadratic formula x
2 + x - 2 = 0
a = 1, b = 1, and c = -2
x = [-b ± √(b
2 - 4ac)] / 2a
x = [- 1 ± √( (1)
2 - 4 × 1 × -2)] / 2 × 1
x = [-1 ± √(1 - 4 × 1 × -2)] / 2
x = [-1 ± √(1 - 4 × -2)] / 2
x = [-1 ± √(1 + 8)] / 2
x = [-1 ± √(9)] / 2
x = (-1 ± 3 ) / 2
x
1 = (-1 + 3 ) / 2
x
1 = (2) / 2
x
1 = 1
x
2 = (-1 - 3 ) / 2
x
2 = (-4 ) / 2
x
2 = -2
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Nov 18, 20 01:20 PM
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