Enter Quadratic equation/inequality below

Hint Number =

Solve the quadratic:

w2+3w-108 = 0

Set up the a, b, and c values:

a = 1, b = 3, c = -108

Quadratic Formula

w  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(3)

-b = -3

Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = 32 - 4 x 1 x -108

Δ = 9 - -432

Δ = 441 <--- Discriminant

Since Δ > 0, we expect two real roots.

Take the square root of Δ

Δ = √(441)

Δ = 21

-b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = -3 + 21

Numerator 1 = 18

-b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = -3 - 21

Numerator 2 = -24

Calculate 2a

Denominator = 2 * a

Denominator = 2 * 1

Denominator = 2

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  18
  2

Solution 1 = 9

Solution 2

Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -24
  2

Solution 2 = -12

Solution Set

(Solution 1, Solution 2) = (9, -12)


Prove our first answer

(9)2 + 3(9) - 108 ? 0

(81) + 27108 ? 0

81 + 27108 ? 0

0 = 0

Prove our second answer

(-12)2 + 3(-12) - 108 ? 0

(144) - 36108 ? 0

144 - 36108 ? 0

0 = 0

Final Answer

(Solution 1, Solution 2) = (9, -12)


You have 2 free calculationss remaining




What is the Answer?
(Solution 1, Solution 2) = (9, -12)
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
Example calculations for the Quadratic Equations and Inequalities Calculator

Quadratic Equations and Inequalities Calculator Video


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