Answer
(Solution 1, Solution 2) = ((3 . 2√2)/1, (3 - 2√2)/1)
↓Steps Explained:↓
Solve the quadratic:
n2-6n+1 = 0
Set up the a, b, and c values:
a = 1, b = -6, c = 1
Quadratic Formula
| n = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(-6)
-b = 6
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = -62 - 4 x 1 x 1
Δ = 36 - 4
Δ = 32 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(32)
√Δ = 4√2
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 6 + 4√2
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 6 - 4√2
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 =;(6 + 4√2)/2
Simplify using GCF
6, 2, and 4 are all divisible by 3
Dividing them all by 2, we get:
3, 1, and 2
Solution 1 = (3 . 2√2)/1
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
Solution 2 = (6 - 4√2)/2
Simplify using GCF
6, 2, and 4 are all divisible by 2
Dividing them all by 2, we get: 3, 1, and 2
Solution 2 = (3 - 2√2)/1
Solution Set
(Solution 1, Solution 2) = ((3 . 2√2)/1, (3 - 2√2)/1)
Final Answer
(Solution 1, Solution 2) = ((3 . 2√2)/1, (3 - 2√2)/1)Related Calculators: Quartic Equations | 3 Point Equation | Monomials