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 in the standard of a quadratic equation
Quadratic Formula is x = (b ± √(b
^{2}  4ac))/2a
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
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

May 19, 19 09:20 AM
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