# Solve using the quadratic formula

This lesson shows how to solve using the quadratic formula. To use the quadratic formula, you must identify a, b and c in the standard of a quadratic equation

Quadratic formula is x = (BC ± v (b2 – 4ac)) / 2

The standard shape is ax2 + bx + c = 0

(1) for 6 x x 2 + 8 + 7 = 0, we get a = 6, b = 8, c = 7

(2) to x 2 + x 8 – 7 = 0, we get a = 1, b = 8, c =-7

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

Example # 1:

Solve using the quadratic formula x x 2 + 8 + 7 = 0.

a = 1, b = 8, c = 7

x = (BC ± v (b2 – 4ac)) / 2

x = (-8 ± v (82-4 × 1 × 7)) / 2 × 1

x = (-8 ± v (64-4 × 1 × 7)) / 2

x = (-8 ± v (64-4 × 7)) / 2

x = (v(64-28) ±-8) / 2

x = (8 ± v (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 4 x 2-11 x – 3 = 0

a = 4, b =-11 and c = – 3

x = (BC ± v (b2 – 4ac)) / 2

x = (-11 ± v ((-11) 2-4 × 4 ×-3)) / 2 × 4

x = (11 ± v (121-4 × 4-3)) / 8

x = (11 ± v (121-4 × – 12)) / 8

x = (11 ± v (121 + 48)) / 8

x = (± 11 v (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 = (BC ± v (b2 – 4ac)) / 2

x = (-1 ± v (2-4 (1) × 1 ×-2)) / 2 × 1

x = (-1 ± v (1-4 × 1-2)) / 2

x = (-1 ± v (× 1-4-2)) / 2

x = (-1 ± v (1 + 8)) / 2

x = (1 ± v (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