Answer
Success!
(Solution 1, Solution 2) = (6, -7)
↓Steps Explained:↓
Solve the quadratic:
x2+x-42 = 0
Set up the a, b, and c values:
a = 1, b = 1, c = -42
Quadratic Formula
| x = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(1)
-b = -1
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 12 - 4 x 1 x -42
Δ = 1 - -168
Δ = 169 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(169)
√Δ = 13
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -1 + 13
Numerator 1 = 12
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -1 - 13
Numerator 2 = -14
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 = 6
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = -7
Solution Set
(Solution 1, Solution 2) = (6, -7)
Prove our first answer
(6)2 + 1(6) - 42 ? 0
(36) + 642 ? 0
36 + 642 ? 0
0 = 0
Prove our second answer
(-7)2 + 1(-7) - 42 ? 0
(49) - 742 ? 0
49 - 742 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (6, -7)Take the Quiz
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