Hint Number =

n2-6n+1 = 0

##### Set up the a, b, and c values:

a = 1, b = -6, c = 1

 n  = -b ± √b2 - 4ac 2a

-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.

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)

(Solution 1, Solution 2) = ((3 . 2√2)/1, (3 - 2√2)/1)

(Solution 1, Solution 2) = ((3 . 2√2)/1, (3 - 2√2)/1)
##### How does the Quadratic Equations and Inequalities Calculator work?
Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

### What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

### What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the square
a technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + k
equation
a statement declaring two mathematical expressions are equal
factor
a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
intercept
parabola
a plane curve which is approximately U-shaped