-2x^2-8x+16+10=0

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Solution for -2x^2-8x+16+10=0 equation: 


Simplifying
-2x2 + -8x + 16 + 10 = 0

Reorder the terms:
16 + 10 + -8x + -2x2 = 0

Combine like terms: 16 + 10 = 26
26 + -8x + -2x2 = 0

Solving
26 + -8x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + -4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
13 + -4x + -1x2 = 0

Solving
13 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13 + 4x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 4x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 4x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 4x + x2 = 0 + 13
4x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
4x + x2 = 13

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 13 + 4

Reorder the terms:
4 + 4x + x2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + 4x + x2 = 17

Factor a perfect square on the left side:
(x + 2)(x + 2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 2) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + 2 = 4.123105626

Simplifying
x + 2 = 4.123105626

Reorder the terms:
2 + x = 4.123105626

Solving
2 + x = 4.123105626

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.123105626 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.123105626 + -2
x = 4.123105626 + -2

Combine like terms: 4.123105626 + -2 = 2.123105626
x = 2.123105626

Simplifying
x = 2.123105626


Subproblem 2
x + 2 = -4.123105626

Simplifying
x + 2 = -4.123105626

Reorder the terms:
2 + x = -4.123105626

Solving
2 + x = -4.123105626

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.123105626 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.123105626 + -2
x = -4.123105626 + -2

Combine like terms: -4.123105626 + -2 = -6.123105626
x = -6.123105626

Simplifying
x = -6.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.123105626, -6.123105626}
Solution
x = {2.123105626, -6.123105626}

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