Solve Quadratic Equations By Formula

Before viewing this page, it would be helpful to learn how to Solve Quadratic Expressions By Factorizing.

Quadratic equations have a variable with a power of 2 and are in the form:

ax2 + bx + c = 0

In the quadratic equation x2 + 9x + 20 = 0,
a = 1
b = 9
c = 20.

The formula to solve a quadratic equation is:

x = –b ± √b2 – 4ac
2a

Example One - Solve by Factorization

Factorize and solve x2 + 9x + 20 = 0

Answer:
x2 + 9x + 20 = 0
( x + 4 ) ( x + 5 ) = 0

Either x + 4 = 0 or x + 5 = 0

If x + 4 + 0
x = –4

If x + 5 = 0
x = –5

x = –4 or –5


Example Two - Solve using the Quadratic Formula

Use the quadratic formula to solve x2 + 9x + 20 = 0

Answer:
a = 1
b = 9
c = 20

x = –9 ± √92 – (4 × 1 × 20)
2 × 1

x = –4 or –5


Example Three

Use the quadratic formula to solve x2 – 3x – 40 = 0

Answer:
a = 1
b = –3
c = –40

x = +3 ± √(–3)2 + (4 × 1 × 40)
2 × 1

x = –5 or 8


Example Four

Use the quadratic formula to solve 3x2 – 11x + 6 = 0

Answer:
a = 3
b = –11
c = 6

x = +11 ± √(–11)2 – (4 × 3 × 6)
2 × 3

x = 4.2 or –0.5

Questions - Solve using the Quadratic Formula

Q1. x2 – 8x + 7 = 0
Q2. x2 – 18x + 81 = 0
Q3. x2 + 3x = 0

Answers:
A1. x = 1 or 7
A2. x = 9
A3. x = 0 or –3