x^2-13x+29=0

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Solution for x^2-13x+29=0 equation:


Simplifying
x2 + -13x + 29 = 0

Reorder the terms:
29 + -13x + x2 = 0

Solving
29 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -13x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + -13x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -13x + x2 = 0 + -29
-13x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
-13x + x2 = -29

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 = -29 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -29 + 42.25

Combine like terms: -29 + 42.25 = 13.25
42.25 + -13x + x2 = 13.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + -6.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

x + -6.5 = 3.640054945 Simplifying x + -6.5 = 3.640054945 Reorder the terms: -6.5 + x = 3.640054945 Solving -6.5 + x = 3.640054945 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 = 3.640054945 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.640054945 + 6.5 x = 3.640054945 + 6.5 Combine like terms: 3.640054945 + 6.5 = 10.140054945 x = 10.140054945 Simplifying x = 10.140054945

Subproblem 2

x + -6.5 = -3.640054945 Simplifying x + -6.5 = -3.640054945 Reorder the terms: -6.5 + x = -3.640054945 Solving -6.5 + x = -3.640054945 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 = -3.640054945 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.640054945 + 6.5 x = -3.640054945 + 6.5 Combine like terms: -3.640054945 + 6.5 = 2.859945055 x = 2.859945055 Simplifying x = 2.859945055

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.140054945, 2.859945055}

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