(4x^2-2x-53)+(2x^2+8x)=

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Solution for (4x^2-2x-53)+(2x^2+8x)= equation: 


Simplifying
(4x2 + -2x + -53) + (2x2 + 8x) = 0

Reorder the terms:
(-53 + -2x + 4x2) + (2x2 + 8x) = 0

Remove parenthesis around (-53 + -2x + 4x2)
-53 + -2x + 4x2 + (2x2 + 8x) = 0

Reorder the terms:
-53 + -2x + 4x2 + (8x + 2x2) = 0

Remove parenthesis around (8x + 2x2)
-53 + -2x + 4x2 + 8x + 2x2 = 0

Reorder the terms:
-53 + -2x + 8x + 4x2 + 2x2 = 0

Combine like terms: -2x + 8x = 6x
-53 + 6x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
-53 + 6x + 6x2 = 0

Solving
-53 + 6x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-8.833333333 + x + x2 = 0

Move the constant term to the right:

Add '8.833333333' to each side of the equation.
-8.833333333 + x + 8.833333333 + x2 = 0 + 8.833333333

Reorder the terms:
-8.833333333 + 8.833333333 + x + x2 = 0 + 8.833333333

Combine like terms: -8.833333333 + 8.833333333 = 0.000000000
0.000000000 + x + x2 = 0 + 8.833333333
x + x2 = 0 + 8.833333333

Combine like terms: 0 + 8.833333333 = 8.833333333
x + x2 = 8.833333333

The x term is x.  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.
 + 0.25 + x2 = 8.833333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 8.833333333 + 0.25

Combine like terms: 8.833333333 + 0.25 = 9.083333333
1.25 + x2 = 9.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9.083333333

Calculate the square root of the right side: 3.013856887

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.013856887 and -3.013856887.


Subproblem 1
x + 0.5 = 3.013856887

Simplifying
x + 0.5 = 3.013856887

Reorder the terms:
0.5 + x = 3.013856887

Solving
0.5 + x = 3.013856887

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 = 3.013856887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.013856887 + -0.5
x = 3.013856887 + -0.5

Combine like terms: 3.013856887 + -0.5 = 2.513856887
x = 2.513856887

Simplifying
x = 2.513856887


Subproblem 2
x + 0.5 = -3.013856887

Simplifying
x + 0.5 = -3.013856887

Reorder the terms:
0.5 + x = -3.013856887

Solving
0.5 + x = -3.013856887

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 = -3.013856887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.013856887 + -0.5
x = -3.013856887 + -0.5

Combine like terms: -3.013856887 + -0.5 = -3.513856887
x = -3.513856887

Simplifying
x = -3.513856887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.513856887, -3.513856887}

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