Answer
Success!
(Solution 1, Solution 2) = (8, -9)
↓Steps Explained:↓
Solve the quadratic:
n2+n-72 = 0
Set up the a, b, and c values:
a = 1, b = 1, c = -72
Quadratic Formula
| n = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(1)
-b = -1
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 12 - 4 x 1 x -72
Δ = 1 - -288
Δ = 289 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(289)
√Δ = 17
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -1 + 17
Numerator 1 = 16
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -1 - 17
Numerator 2 = -18
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 = 8
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = -9
Solution Set
(Solution 1, Solution 2) = (8, -9)
Prove our first answer
(8)2 + 1(8) - 72 ? 0
(64) + 872 ? 0
64 + 872 ? 0
0 = 0
Prove our second answer
(-9)2 + 1(-9) - 72 ? 0
(81) - 972 ? 0
81 - 972 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (8, -9)Take the Quiz
Related Calculators: Quartic Equations | 3 Point Equation | Monomials