Solve the quadratic:
w2-31w+238 = 0
Set up the a, b, and c values:
a = 1, b = -31, c = 238
Quadratic Formula
| w = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(-31)
-b = 31
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = -312 - 4 x 1 x 238
Δ = 961 - 952
Δ = 9 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(9)
√Δ = 3
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 31 + 3
Numerator 1 = 34
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 31 - 3
Numerator 2 = 28
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 34 |
| 2 |
Solution 1 = 17
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | 28 |
| 2 |
Solution 2 = 14
Solution Set
(Solution 1, Solution 2) = (17, 14)
Prove our first answer
(17)2 - 31(17) + 238 ? 0
(289) - 527238 ? 0
289 - 527238 ? 0
0 = 0
Prove our second answer
(14)2 - 31(14) + 238 ? 0
(196) - 434238 ? 0
196 - 434238 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (17, 14)
