-x^2+13x-13.3=0

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Solution for -x^2+13x-13.3=0 equation:


Simplifying
-1x2 + 13x + -13.3 = 0

Reorder the terms:
-13.3 + 13x + -1x2 = 0

Solving
-13.3 + 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'.
13.3 + -13x + x2 = 0

Move the constant term to the right:

Add '-13.3' to each side of the equation.
13.3 + -13x + -13.3 + x2 = 0 + -13.3

Reorder the terms:
13.3 + -13.3 + -13x + x2 = 0 + -13.3

Combine like terms: 13.3 + -13.3 = 0.0
0.0 + -13x + x2 = 0 + -13.3
-13x + x2 = 0 + -13.3

Combine like terms: 0 + -13.3 = -13.3
-13x + x2 = -13.3

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 = -13.3 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -13.3 + 42.25

Combine like terms: -13.3 + 42.25 = 28.95
42.25 + -13x + x2 = 28.95

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 28.95

Calculate the square root of the right side: 5.380520421

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.380520421 and -5.380520421.

Subproblem 1

x + -6.5 = 5.380520421 Simplifying x + -6.5 = 5.380520421 Reorder the terms: -6.5 + x = 5.380520421 Solving -6.5 + x = 5.380520421 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 = 5.380520421 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.380520421 + 6.5 x = 5.380520421 + 6.5 Combine like terms: 5.380520421 + 6.5 = 11.880520421 x = 11.880520421 Simplifying x = 11.880520421

Subproblem 2

x + -6.5 = -5.380520421 Simplifying x + -6.5 = -5.380520421 Reorder the terms: -6.5 + x = -5.380520421 Solving -6.5 + x = -5.380520421 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 = -5.380520421 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.380520421 + 6.5 x = -5.380520421 + 6.5 Combine like terms: -5.380520421 + 6.5 = 1.119479579 x = 1.119479579 Simplifying x = 1.119479579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.880520421, 1.119479579}

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