-x^2+8x+13=0

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Solution for -x^2+8x+13=0 equation: 


Simplifying
-1x2 + 8x + 13 = 0

Reorder the terms:
13 + 8x + -1x2 = 0

Solving
13 + 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'.
-13 + -8x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -8x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -8x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -8x + x2 = 0 + 13
-8x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-8x + x2 = 13

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 = 13 + 16

Reorder the terms:
16 + -8x + x2 = 13 + 16

Combine like terms: 13 + 16 = 29
16 + -8x + x2 = 29

Factor a perfect square on the left side:
(x + -4)(x + -4) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -4) equal to 5.385164807 and -5.385164807.


Subproblem 1
x + -4 = 5.385164807

Simplifying
x + -4 = 5.385164807

Reorder the terms:
-4 + x = 5.385164807

Solving
-4 + x = 5.385164807

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 = 5.385164807 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.385164807 + 4
x = 5.385164807 + 4

Combine like terms: 5.385164807 + 4 = 9.385164807
x = 9.385164807

Simplifying
x = 9.385164807


Subproblem 2
x + -4 = -5.385164807

Simplifying
x + -4 = -5.385164807

Reorder the terms:
-4 + x = -5.385164807

Solving
-4 + x = -5.385164807

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 = -5.385164807 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.385164807 + 4
x = -5.385164807 + 4

Combine like terms: -5.385164807 + 4 = -1.385164807
x = -1.385164807

Simplifying
x = -1.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.385164807, -1.385164807}

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