-2x^2+36=-2x+9

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Solution for -2x^2+36=-2x+9 equation:


Simplifying
-2x2 + 36 = -2x + 9

Reorder the terms:
36 + -2x2 = -2x + 9

Reorder the terms:
36 + -2x2 = 9 + -2x

Solving
36 + -2x2 = 9 + -2x

Solving for variable 'x'.

Reorder the terms:
36 + -9 + 2x + -2x2 = 9 + -2x + -9 + 2x

Combine like terms: 36 + -9 = 27
27 + 2x + -2x2 = 9 + -2x + -9 + 2x

Reorder the terms:
27 + 2x + -2x2 = 9 + -9 + -2x + 2x

Combine like terms: 9 + -9 = 0
27 + 2x + -2x2 = 0 + -2x + 2x
27 + 2x + -2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
27 + 2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-13.5 + -1x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -1x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -1x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -1x + x2 = 0 + 13.5
-1x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-1x + x2 = 13.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 13.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 13.5 + 0.25

Combine like terms: 13.5 + 0.25 = 13.75
0.25 + -1x + x2 = 13.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.708099244 and -3.708099244.

Subproblem 1

x + -0.5 = 3.708099244 Simplifying x + -0.5 = 3.708099244 Reorder the terms: -0.5 + x = 3.708099244 Solving -0.5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.708099244 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.708099244 + 0.5 x = 3.708099244 + 0.5 Combine like terms: 3.708099244 + 0.5 = 4.208099244 x = 4.208099244 Simplifying x = 4.208099244

Subproblem 2

x + -0.5 = -3.708099244 Simplifying x + -0.5 = -3.708099244 Reorder the terms: -0.5 + x = -3.708099244 Solving -0.5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.708099244 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.708099244 + 0.5 x = -3.708099244 + 0.5 Combine like terms: -3.708099244 + 0.5 = -3.208099244 x = -3.208099244 Simplifying x = -3.208099244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.208099244, -3.208099244}

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