-x^2+8x+4=5

Solution for -x^2+8x+4=5 equation:

Simplifying
-1x2 + 8x + 4 = 5

Reorder the terms:
4 + 8x + -1x2 = 5

Solving
4 + 8x + -1x2 = 5

Solving for variable 'x'.

Reorder the terms:
4 + -5 + 8x + -1x2 = 5 + -5

Combine like terms: 4 + -5 = -1
-1 + 8x + -1x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-1 + 8x + -1x2 = 0

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

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

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -8x + -1 + x2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + -8x + x2 = 0 + -1
-8x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8x + x2 = -1

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 = -1 + 16

Reorder the terms:
16 + -8x + x2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + -8x + x2 = 15

Factor a perfect square on the left side:
(x + -4)(x + -4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -4) equal to 3.872983346 and -3.872983346.

Subproblem 1
x + -4 = 3.872983346

Simplifying
x + -4 = 3.872983346

Reorder the terms:
-4 + x = 3.872983346

Solving
-4 + x = 3.872983346

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 = 3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.872983346 + 4
x = 3.872983346 + 4

Combine like terms: 3.872983346 + 4 = 7.872983346
x = 7.872983346

Simplifying
x = 7.872983346

Subproblem 2
x + -4 = -3.872983346

Simplifying
x + -4 = -3.872983346

Reorder the terms:
-4 + x = -3.872983346

Solving
-4 + x = -3.872983346

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 = -3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.872983346 + 4
x = -3.872983346 + 4

Combine like terms: -3.872983346 + 4 = 0.127016654
x = 0.127016654

Simplifying
x = 0.127016654

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.872983346, 0.127016654}