Solve Quadratic Equation for x^2

Publish date: 2024-06-10
Solve Quadratic Equation for x^2 - 10x + 16 = 0

Solve Quadratic Equation for x^2 - 10x + 16 = 0

Image to Crop Solve the quadratic equation
x2-10x+16 = 0

We have our a, b, and c values:
a = 1, b = -10, c = 16

Solve the quadratic equation
x2 - 10x + 16=

Quadratic Formula

x  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(-10)
-b = 10

Calculate the discriminant Δ

Δ = b2 - 4ac:
Δ = -102 - 4 x 1 x 16
Δ = 100 - 64
Δ = 36 <--- Discriminant
Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(36)
√Δ = 6

-b + Δ:

Numerator 1 = -b + √Δ
Numerator 1 = 10 + 6
Numerator 1 = 16

-b - Δ:

Numerator 2 = -b - √Δ
Numerator 2 = 10 - 6
Numerator 2 = 4

Calculate 2a

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

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  16
  2

  Solution 1  =  8
Solution 2  =  Numerator 2
  Denominator

Solution 2  =  4
  2

  Solution 2  =  2

Solution Set

(Solution 1, Solution 2) = (8, 2)

Prove our first answer

(8)2 - 10(8) + 16 ? 0
(64) - 8016 ? 0
64 - 8016 ? 0
0 = 0

Prove our second answer

(2)2 - 10(2) + 16 ? 0
(4) - 2016 ? 0
4 - 2016 ? 0
0 = 0

(Solution 1, Solution 2) = (8, 2)


What is the Answer?

(Solution 1, Solution 2) = (8, 2)

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 squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora 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.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

Example calculations for the Quadratic Equations and Inequalities Calculator

Quadratic Equations and Inequalities Calculator Video


Tags:

Add This Calculator To Your Website

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfpsKisNGaq6KbXqW1sYvNrqR2sFVqknN3jGRoabBbWn%2BDd5BvYl5rdGB9Z7zLdoqopKaaeJLBwJ2pmqyZmHiGvdSaq6Knnlu1qrrTp6ymdWA%3D