-x^2+13x-2=0

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


Simplifying
-1x2 + 13x + -2 = 0

Reorder the terms:
-2 + 13x + -1x2 = 0

Solving
-2 + 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'.
2 + -13x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -13x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -13x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -13x + x2 = 0 + -2
-13x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-13x + x2 = -2

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 = -2 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -2 + 42.25

Combine like terms: -2 + 42.25 = 40.25
42.25 + -13x + x2 = 40.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

x + -6.5 = 6.34428877 Simplifying x + -6.5 = 6.34428877 Reorder the terms: -6.5 + x = 6.34428877 Solving -6.5 + x = 6.34428877 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 = 6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.34428877 + 6.5 x = 6.34428877 + 6.5 Combine like terms: 6.34428877 + 6.5 = 12.84428877 x = 12.84428877 Simplifying x = 12.84428877

Subproblem 2

x + -6.5 = -6.34428877 Simplifying x + -6.5 = -6.34428877 Reorder the terms: -6.5 + x = -6.34428877 Solving -6.5 + x = -6.34428877 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 = -6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.34428877 + 6.5 x = -6.34428877 + 6.5 Combine like terms: -6.34428877 + 6.5 = 0.15571123 x = 0.15571123 Simplifying x = 0.15571123

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.84428877, 0.15571123}

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