2x^2-50=-x^2+2x+36

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Solution for 2x^2-50=-x^2+2x+36 equation: 


Simplifying
2x2 + -50 = -1x2 + 2x + 36

Reorder the terms:
-50 + 2x2 = -1x2 + 2x + 36

Reorder the terms:
-50 + 2x2 = 36 + 2x + -1x2

Solving
-50 + 2x2 = 36 + 2x + -1x2

Solving for variable 'x'.

Reorder the terms:
-50 + -36 + -2x + 2x2 + x2 = 36 + 2x + -1x2 + -36 + -2x + x2

Combine like terms: -50 + -36 = -86
-86 + -2x + 2x2 + x2 = 36 + 2x + -1x2 + -36 + -2x + x2

Combine like terms: 2x2 + x2 = 3x2
-86 + -2x + 3x2 = 36 + 2x + -1x2 + -36 + -2x + x2

Reorder the terms:
-86 + -2x + 3x2 = 36 + -36 + 2x + -2x + -1x2 + x2

Combine like terms: 36 + -36 = 0
-86 + -2x + 3x2 = 0 + 2x + -2x + -1x2 + x2
-86 + -2x + 3x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
-86 + -2x + 3x2 = 0 + -1x2 + x2
-86 + -2x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-86 + -2x + 3x2 = 0

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

Divide each side by '3'.
-28.66666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '28.66666667' to each side of the equation.
-28.66666667 + -0.6666666667x + 28.66666667 + x2 = 0 + 28.66666667

Reorder the terms:
-28.66666667 + 28.66666667 + -0.6666666667x + x2 = 0 + 28.66666667

Combine like terms: -28.66666667 + 28.66666667 = 0.00000000
0.00000000 + -0.6666666667x + x2 = 0 + 28.66666667
-0.6666666667x + x2 = 0 + 28.66666667

Combine like terms: 0 + 28.66666667 = 28.66666667
-0.6666666667x + x2 = 28.66666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 28.66666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 28.66666667 + 0.1111111112

Combine like terms: 28.66666667 + 0.1111111112 = 28.7777777812
0.1111111112 + -0.6666666667x + x2 = 28.7777777812

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 28.7777777812

Calculate the square root of the right side: 5.364492313

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 5.364492313 and -5.364492313.


Subproblem 1
x + -0.3333333334 = 5.364492313

Simplifying
x + -0.3333333334 = 5.364492313

Reorder the terms:
-0.3333333334 + x = 5.364492313

Solving
-0.3333333334 + x = 5.364492313

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 5.364492313 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 5.364492313 + 0.3333333334
x = 5.364492313 + 0.3333333334

Combine like terms: 5.364492313 + 0.3333333334 = 5.6978256464
x = 5.6978256464

Simplifying
x = 5.6978256464


Subproblem 2
x + -0.3333333334 = -5.364492313

Simplifying
x + -0.3333333334 = -5.364492313

Reorder the terms:
-0.3333333334 + x = -5.364492313

Solving
-0.3333333334 + x = -5.364492313

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -5.364492313 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -5.364492313 + 0.3333333334
x = -5.364492313 + 0.3333333334

Combine like terms: -5.364492313 + 0.3333333334 = -5.0311589796
x = -5.0311589796

Simplifying
x = -5.0311589796


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.6978256464, -5.0311589796}

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