## Enter Quadratic equation/inequality below

Hint Number =

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

-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.

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)

##### What is the Answer?
(Solution 1, Solution 2) = ((5 . 1√29)/1, (5 - 1√29)/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
* Factor 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
quadratic
Polynomials with a maximum term degree as the second degree
quadratic equations and inequalities
rational root
vertex
Highest point or where 2 curves meet

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