-x^2+13x-4=0

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Solution for -x^2+13x-4=0 equation: 


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

Reorder the terms:
-4 + 13x + -1x2 = 0

Solving
-4 + 13x + -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'.
4 + -13x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -4 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25
42.25 + -13x + x2 = 38.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + -6.5 = 6.184658438

Simplifying
x + -6.5 = 6.184658438

Reorder the terms:
-6.5 + x = 6.184658438

Solving
-6.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.184658438 + 6.5
x = 6.184658438 + 6.5

Combine like terms: 6.184658438 + 6.5 = 12.684658438
x = 12.684658438

Simplifying
x = 12.684658438


Subproblem 2
x + -6.5 = -6.184658438

Simplifying
x + -6.5 = -6.184658438

Reorder the terms:
-6.5 + x = -6.184658438

Solving
-6.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.184658438 + 6.5
x = -6.184658438 + 6.5

Combine like terms: -6.184658438 + 6.5 = 0.315341562
x = 0.315341562

Simplifying
x = 0.315341562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.684658438, 0.315341562}

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