x^2-13x+11=

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Solution for x^2-13x+11= equation:


Simplifying
x2 + -13x + 11 = 0

Reorder the terms:
11 + -13x + x2 = 0

Solving
11 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -13x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -13x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -13x + x2 = 0 + -11
-13x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-13x + x2 = -11

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 = -11 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -11 + 42.25

Combine like terms: -11 + 42.25 = 31.25
42.25 + -13x + x2 = 31.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

x + -6.5 = 5.590169944 Simplifying x + -6.5 = 5.590169944 Reorder the terms: -6.5 + x = 5.590169944 Solving -6.5 + x = 5.590169944 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 = 5.590169944 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.590169944 + 6.5 x = 5.590169944 + 6.5 Combine like terms: 5.590169944 + 6.5 = 12.090169944 x = 12.090169944 Simplifying x = 12.090169944

Subproblem 2

x + -6.5 = -5.590169944 Simplifying x + -6.5 = -5.590169944 Reorder the terms: -6.5 + x = -5.590169944 Solving -6.5 + x = -5.590169944 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 = -5.590169944 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.590169944 + 6.5 x = -5.590169944 + 6.5 Combine like terms: -5.590169944 + 6.5 = 0.909830056 x = 0.909830056 Simplifying x = 0.909830056

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.090169944, 0.909830056}

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