Answer:
- x1 = -9 , x2 = 9
- x1 = -2 , x2 = 15
- x1 = -3 , x2 = -2
- m1 = 4, m2 = 3/2
- The square root of a negative number does not exist in the set of real numbers
Step-by-step explanation:
1. Square Roots
x² - 81 = 0
x² = 81
√x² = √81
x = ±9
x1 = -9 , x2 = 9
2. Factoring
x² - 13x = 30
x² - 13x - 30 = 0
x² + 2x - 15x - 30 = 0
x × ( x + 2) - 15(x + 2) = 0
(x + 2) × (x - 15) = 0
x + 2 = 0
x1 = -2
x - 15 = 0
x2 = 15
3. Factoring
x² + 5x + 6 = 0
x² + 3x + 2x + 6 = 0
x × (x + 3) + 2(x + 3) = 0
(x + 3) × (x + 2) = 0
x + 3 = 0
x1 = -3
x + 2 = 0
x2 = -2
4. Completing the Square
2m² - 11m + 12 = 0
2m² - 11m = -12
2m² ÷ 2 - 11m ÷ 2 = -12 ÷ 2
m² - 11/2m = -6
m² - 11/2m + 121/6 = -6 + 121/6
(m - 11/4)² = 25/16
√(m - 11/4)² = √25/16
m - 11/4 = ±5/4
m - 11/4 = 5/4
m = 5/4 + 11/4
m = 16/4 ÷ 4/4
m1 = 4
m - 11/4 = -5/4
m = -5/4 + 11/4
m = 6/4 ÷ 2/2
m2 = 3/2
5. Quadratic Formula
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