Answer
(Solution 1, Solution 2) = (9, -12)
↓Steps Explained:↓
Solve the quadratic:
w2+3w-108 = 0
Set up the a, b, and c values:
a = 1, b = 3, c = -108
Quadratic Formula
| w = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(3)
-b = -3
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 32 - 4 x 1 x -108
Δ = 9 - -432
Δ = 441 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(441)
√Δ = 21
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -3 + 21
Numerator 1 = 18
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -3 - 21
Numerator 2 = -24
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 = 9
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = -12
Solution Set
(Solution 1, Solution 2) = (9, -12)
Prove our first answer
(9)2 + 3(9) - 108 ? 0
(81) + 27108 ? 0
81 + 27108 ? 0
0 = 0
Prove our second answer
(-12)2 + 3(-12) - 108 ? 0
(144) - 36108 ? 0
144 - 36108 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (9, -12)Related Calculators: Quartic Equations | 3 Point Equation | Monomials