x^2-13x+7=0

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Solution for x^2-13x+7=0 equation:


Simplifying
x2 + -13x + 7 = 0

Reorder the terms:
7 + -13x + x2 = 0

Solving
7 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -13x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -13x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -13x + x2 = 0 + -7
-13x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-13x + x2 = -7

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 = -7 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -7 + 42.25

Combine like terms: -7 + 42.25 = 35.25
42.25 + -13x + x2 = 35.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.937171044 and -5.937171044.

Subproblem 1

x + -6.5 = 5.937171044 Simplifying x + -6.5 = 5.937171044 Reorder the terms: -6.5 + x = 5.937171044 Solving -6.5 + x = 5.937171044 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 = 5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.937171044 + 6.5 x = 5.937171044 + 6.5 Combine like terms: 5.937171044 + 6.5 = 12.437171044 x = 12.437171044 Simplifying x = 12.437171044

Subproblem 2

x + -6.5 = -5.937171044 Simplifying x + -6.5 = -5.937171044 Reorder the terms: -6.5 + x = -5.937171044 Solving -6.5 + x = -5.937171044 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 = -5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.937171044 + 6.5 x = -5.937171044 + 6.5 Combine like terms: -5.937171044 + 6.5 = 0.562828956 x = 0.562828956 Simplifying x = 0.562828956

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.437171044, 0.562828956}

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