Quadratic equations have x² as the highest power. They often have two solutions and their graphs are parabolas.
ax² + bx + c = 0
Where a ≠ 0, and a, b, c are constants
x² - 4 = 0
Simple quadratic
x² + 5x + 6 = 0
Factorable quadratic
2x² - 3x - 1 = 0
Use quadratic formula
When possible, factor the quadratic into two brackets and solve each factor = 0.
Step 1: Find two numbers that multiply to 6 and add to 5
Numbers: 2 and 3 (2 × 3 = 6, 2 + 3 = 5)
Step 2: Write as factors
(x + 2)(x + 3) = 0
Step 3: Solve each factor
x + 2 = 0 → x = -2
x + 3 = 0 → x = -3
Solutions: x = -2 or x = -3
When factoring is difficult, use the quadratic formula to find solutions.
x = (-b ± √(b² - 4ac)) / 2a
a = 1, b = -3, c = -4
x = (3 ± √(9 + 16)) / 2 = (3 ± √25) / 2 = (3 ± 5) / 2
x = (3 + 5)/2 = 4 or x = (3 - 5)/2 = -1
1. Solve by factoring: x² - 5x + 6 = 0