2.232x^2-4.114x=6.219

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Solution for 2.232x^2-4.114x=6.219 equation:


Simplifying
2.232x2 + -4.114x = 6.219

Reorder the terms:
-4.114x + 2.232x2 = 6.219

Solving
-4.114x + 2.232x2 = 6.219

Solving for variable 'x'.

Reorder the terms:
-6.219 + -4.114x + 2.232x2 = 6.219 + -6.219

Combine like terms: 6.219 + -6.219 = 0.000
-6.219 + -4.114x + 2.232x2 = 0.000

Begin completing the square.  Divide all terms by
2.232 the coefficient of the squared term: 

Divide each side by '2.232'.
-2.786290323 + -1.843189964x + x2 = 0

Move the constant term to the right:

Add '2.786290323' to each side of the equation.
-2.786290323 + -1.843189964x + 2.786290323 + x2 = 0 + 2.786290323

Reorder the terms:
-2.786290323 + 2.786290323 + -1.843189964x + x2 = 0 + 2.786290323

Combine like terms: -2.786290323 + 2.786290323 = 0.000000000
0.000000000 + -1.843189964x + x2 = 0 + 2.786290323
-1.843189964x + x2 = 0 + 2.786290323

Combine like terms: 0 + 2.786290323 = 2.786290323
-1.843189964x + x2 = 2.786290323

The x term is -1.843189964x.  Take half its coefficient (-0.921594982).
Square it (0.8493373108) and add it to both sides.

Add '0.8493373108' to each side of the equation.
-1.843189964x + 0.8493373108 + x2 = 2.786290323 + 0.8493373108

Reorder the terms:
0.8493373108 + -1.843189964x + x2 = 2.786290323 + 0.8493373108

Combine like terms: 2.786290323 + 0.8493373108 = 3.6356276338
0.8493373108 + -1.843189964x + x2 = 3.6356276338

Factor a perfect square on the left side:
(x + -0.921594982)(x + -0.921594982) = 3.6356276338

Calculate the square root of the right side: 1.906732187

Break this problem into two subproblems by setting 
(x + -0.921594982) equal to 1.906732187 and -1.906732187.

Subproblem 1

x + -0.921594982 = 1.906732187 Simplifying x + -0.921594982 = 1.906732187 Reorder the terms: -0.921594982 + x = 1.906732187 Solving -0.921594982 + x = 1.906732187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921594982' to each side of the equation. -0.921594982 + 0.921594982 + x = 1.906732187 + 0.921594982 Combine like terms: -0.921594982 + 0.921594982 = 0.000000000 0.000000000 + x = 1.906732187 + 0.921594982 x = 1.906732187 + 0.921594982 Combine like terms: 1.906732187 + 0.921594982 = 2.828327169 x = 2.828327169 Simplifying x = 2.828327169

Subproblem 2

x + -0.921594982 = -1.906732187 Simplifying x + -0.921594982 = -1.906732187 Reorder the terms: -0.921594982 + x = -1.906732187 Solving -0.921594982 + x = -1.906732187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921594982' to each side of the equation. -0.921594982 + 0.921594982 + x = -1.906732187 + 0.921594982 Combine like terms: -0.921594982 + 0.921594982 = 0.000000000 0.000000000 + x = -1.906732187 + 0.921594982 x = -1.906732187 + 0.921594982 Combine like terms: -1.906732187 + 0.921594982 = -0.985137205 x = -0.985137205 Simplifying x = -0.985137205

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.828327169, -0.985137205}

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