Solve the quadratic:
t2+10t-816 = 0
Set up the a, b, and c values:
a = 1, b = 10, c = -816
Quadratic Formula
| t = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(10)
-b = -10
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 102 - 4 x 1 x -816
Δ = 100 - -3264
Δ = 3364 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(3364)
√Δ = 58
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -10 + 58
Numerator 1 = 48
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -10 - 58
Numerator 2 = -68
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 48 |
| 2 |
Solution 1 = 24
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | -68 |
| 2 |
Solution 2 = -34
Solution Set
(Solution 1, Solution 2) = (24, -34)
Prove our first answer
(24)2 + 10(24) - 816 ? 0
(576) + 240816 ? 0
576 + 240816 ? 0
0 = 0
Prove our second answer
(-34)2 + 10(-34) - 816 ? 0
(1156) - 340816 ? 0
1156 - 340816 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (24, -34)
