Answer
Success!
(Solution 1, Solution 2) = (7, -4)
↓Steps Explained:↓
Solve the quadratic:
n2-3n-28 = 0
Set up the a, b, and c values:
a = 1, b = -3, c = -28
Quadratic Formula
| n = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(-3)
-b = 3
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = -32 - 4 x 1 x -28
Δ = 9 - -112
Δ = 121 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(121)
√Δ = 11
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 3 + 11
Numerator 1 = 14
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 3 - 11
Numerator 2 = -8
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 = 7
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = -4
Solution Set
(Solution 1, Solution 2) = (7, -4)
Prove our first answer
(7)2 - 3(7) - 28 ? 0
(49) - 2128 ? 0
49 - 2128 ? 0
0 = 0
Prove our second answer
(-4)2 - 3(-4) - 28 ? 0
(16) + 1228 ? 0
16 + 1228 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (7, -4)Take the Quiz
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