Solve the quadratic:
n2+n = 20
The quadratic you entered is not in standard form:
ax2 + bx + c = 0
Subtract 20 from both sides
n2+n - 20 = 20 - 20n2+n - 20 = 0
Set up the a, b, and c values:
a = 1, b = 1, c = -20
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 -20
Δ = 1 - -80
Δ = 81 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(81)
√Δ = 9
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -1 + 9
Numerator 1 = 8
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -1 - 9
Numerator 2 = -10
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 8 |
| 2 |
Solution 1 = 4
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | -10 |
| 2 |
Solution 2 = -5
Solution Set
(Solution 1, Solution 2) = (4, -5)
Prove our first answer
(4)2 + 1(4) - 20 ? 0
(16) + 420 ? 0
16 + 420 ? 0
0 = 0
Prove our second answer
(-5)2 + 1(-5) - 20 ? 0
(25) - 520 ? 0
25 - 520 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (4, -5)
