Solve the quadratic:
n2+n-650 = 0
Set up the a, b, and c values:
a = 1, b = 1, c = -650
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 -650
Δ = 1 - -2600
Δ = 2601 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(2601)
√Δ = 51
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -1 + 51
Numerator 1 = 50
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -1 - 51
Numerator 2 = -52
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 50 |
| 2 |
Solution 1 = 25
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | -52 |
| 2 |
Solution 2 = -26
Solution Set
(Solution 1, Solution 2) = (25, -26)
Prove our first answer
(25)2 + 1(25) - 650 ? 0
(625) + 25650 ? 0
625 + 25650 ? 0
0 = 0
Prove our second answer
(-26)2 + 1(-26) - 650 ? 0
(676) - 26650 ? 0
676 - 26650 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (25, -26)
