Solve Quadratic Equation for 2n^2+4n+4=290

Solve the quadratic equation
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

Simplifying, we get:

2n²+4n-286 = 0

We have our a, b, and c values:
a = 2, b = 4, c = -286

Solve the quadratic equation
2n² + 4n - 286=

Quadratic Formula

n =	-b ± √b² - 4ac
	2a

Calculate -b

-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.

Take the square root of Δ

√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 =	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

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 = ax^{2^{+ 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

Example calculations for the Quadratic Equations and Inequalities Calculator

Quadratic Equations and Inequalities Calculator Video

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