Solve the quadratic:
x2-10x-4 = 0
Set up the a, b, and c values:
a = 1, b = -10, c = -4
Quadratic Formula
| x = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(-10)
-b = 10
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = -102 - 4 x 1 x -4
Δ = 100 - -16
Δ = 116 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(116)
√Δ = 2√29
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 10 + 2√29
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 10 - 2√29
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 =;(10 + 2√29)/2
Simplify using GCF
10, 2, and 2 are all divisible by 3
Dividing them all by 2, we get:
5, 1, and 1
Solution 1 = (5 . 1√29)/1
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = (10 - 2√29)/2
Simplify using GCF
10, 2, and 2 are all divisible by 2
Dividing them all by 2, we get: 5, 1, and 1
Solution 2 = (5 - 1√29)/1
Solution Set
(Solution 1, Solution 2) = ((5 . 1√29)/1, (5 - 1√29)/1)
Final Answer
(Solution 1, Solution 2) = ((5 . 1√29)/1, (5 - 1√29)/1)
