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.
Solve using the quadratic formula
Solve using the quadratic formula
You can also write the quadratic formula as x = [-b ± √(b2 - 4ac)]/2a

How to identify a, b, and c

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

More examples showing how to solve using the quadratic formula

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. Introduction to Physics

    Nov 18, 20 01:20 PM

    Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

    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.