-x^2+8x+2=0

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


Simplifying
-1x2 + 8x + 2 = 0

Reorder the terms:
2 + 8x + -1x2 = 0

Solving
2 + 8x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-2 + -8x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8x + 2 + x2 = 0 + 2

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

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 2 + 16

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

Combine like terms: 2 + 16 = 18
16 + -8x + x2 = 18

Factor a perfect square on the left side:
(x + -4)(x + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -4 = 4.242640687

Simplifying
x + -4 = 4.242640687

Reorder the terms:
-4 + x = 4.242640687

Solving
-4 + x = 4.242640687

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.242640687 + 4
x = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
x = 8.242640687

Simplifying
x = 8.242640687


Subproblem 2
x + -4 = -4.242640687

Simplifying
x + -4 = -4.242640687

Reorder the terms:
-4 + x = -4.242640687

Solving
-4 + x = -4.242640687

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.242640687 + 4
x = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
x = -0.242640687

Simplifying
x = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.242640687, -0.242640687}

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