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 ± √(b2 - 4ac))/2a


The standard form is ax2 + bx + c = 0

1) for 6x2 + 8x + 7 = 0 we get a = 6, b = 8, and c = 7

2) for x2 + 8x - 7 = 0 we get a = 1, b = 8, and c = -7

2) for -x2 - 8x + 7 = 0 we get a = -1, b = -8, and c = 7


Example #1:


Solve using the quadratic formula x2 + 8x + 7 = 0

a = 1, b = 8, and c = 7

x = (-b ± √(b2 - 4ac)) / 2a

x = (-8 ± √(82 - 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

x1 = (-8 + 6 ) / 2

x1 = (-2 ) / 2

x1 = -1

x2 = (-8 - 6 ) / 2

x2 = (-14 ) / 2

x2 = -7


Example #2:


Solve using the quadratic formula 4x2 - 11x - 3 = 0

a = 4, b = -11, and c = -3

x = (-b ± √(b2 - 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

x1 = (11 + 13 ) / 8

x1 = (24 ) / 8

x1 = 3

x2 = (11 - 13 ) / 8

x2 = (-2 ) / 8

x2 = -1/4


Example #3:


Solve using the quadratic formula x2 + x - 2 = 0

a = 1, b = 1, and c = -2

x = (-b ± √(b2 - 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

x1 = (-1 + 3 ) / 2

x1 = (2) / 2

x1 = 1

x2 = (-1 - 3 ) / 2

x2 = (-4 ) / 2

x2 = -2

Recent Articles

  1. How to Write an Inequality

    Dec 12, 19 07:51 AM

    Learn how to write an inequality quickly with this easy to follow math lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.