Solve the quadratic:
w2+5w-546 = 0
Set up the a, b, and c values:
a = 1, b = 5, c = -546
Quadratic Formula
| w = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(5)
-b = -5
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 52 - 4 x 1 x -546
Δ = 25 - -2184
Δ = 2209 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(2209)
√Δ = 47
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -5 + 47
Numerator 1 = 42
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -5 - 47
Numerator 2 = -52
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 42 |
| 2 |
Solution 1 = 21
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | -52 |
| 2 |
Solution 2 = -26
Solution Set
(Solution 1, Solution 2) = (21, -26)
Prove our first answer
(21)2 + 5(21) - 546 ? 0
(441) + 105546 ? 0
441 + 105546 ? 0
0 = 0
Prove our second answer
(-26)2 + 5(-26) - 546 ? 0
(676) - 130546 ? 0
676 - 130546 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (21, -26)
