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Solve Quadratic Equation for w^2-31w+238=0

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Solve the quadratic equation
w2-31w+238 = 0

We have our a, b, and c values:
a = 1, b = -31, c = 238

Solve the quadratic equation
w2 - 31w + 238=

Quadratic Formula

w  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(-31)
-b = 31

Calculate the discriminant Δ

Δ = b2 - 4ac:
Δ = -312 - 4 x 1 x 238
Δ = 961 - 952
Δ = 9 <--- Discriminant
Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(9)
√Δ = 3

-b + Δ:

Numerator 1 = -b + √Δ
Numerator 1 = 31 + 3
Numerator 1 = 34

-b - Δ:

Numerator 2 = -b - √Δ
Numerator 2 = 31 - 3
Numerator 2 = 28

Calculate 2a

Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  34
  2

  Solution 1  =  17

Solution 2  =  Numerator 2
  Denominator

Solution 2  =  28
  2

  Solution 2  =  14

Solution Set

(Solution 1, Solution 2) = (17, 14)

Prove our first answer

(17)2 - 31(17) + 238 ? 0
(289) - 527238 ? 0
289 - 527238 ? 0
0 = 0

Prove our second answer

(14)2 - 31(14) + 238 ? 0
(196) - 434238 ? 0
196 - 434238 ? 0
0 = 0






What is the Answer?

(Solution 1, Solution 2) = (17, 14)

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

  1. 4x^2+11x-3
  2. a^2-a+6
  3. x^2 + 7x + 6>=0
  4. x^2+2x=35

Quadratic Equations and Inequalities Calculator Video


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