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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