## Enter Quadratic equation/inequality below

Hint Number =

2n2+4n+4 = 290

The quadratic you entered is not in standard form:
ax2 + bx + c = 0

##### Subtract 290 from both sides

2n2+4n+4 - 290 = 290 - 290

2n2+4n-286 = 0

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

a = 2, b = 4, c = -286

 n  = -b ± √b2 - 4ac 2a

-b = -(4)

-b = -4

##### Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = 42 - 4 x 2 x -286

Δ = 16 - -2288

Δ = 2304 <--- Discriminant

Since Δ > 0, we expect two real roots.

Δ = √(2304)

Δ = 48

##### -b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = -4 + 48

Numerator 1 = 44

##### -b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = -4 - 48

Numerator 2 = -52

##### Calculate 2a

Denominator = 2 * a

Denominator = 2 * 2

Denominator = 4

##### Find Solutions

 Solution 1  = Numerator 1 Denominator

 Solution 1  = 44 4

Solution 1 = 11

##### Solution 2

 Solution 2  = Numerator 2 Denominator

 Solution 2  = -52 4

Solution 2 = -13

##### Solution Set

(Solution 1, Solution 2) = (11, -13)

##### Prove our first answer

(11)2 + 4(11) - 286 ? 0

(121) + 44286 ? 0

242 + 44286 ? 0

0 = 0

##### Prove our second answer

(-13)2 + 4(-13) - 286 ? 0

(169) - 52286 ? 0

338 - 52286 ? 0

0 = 0

(Solution 1, Solution 2) = (11, -13)

##### What is the Answer?
(Solution 1, Solution 2) = (11, -13)
##### 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