y^2-13y+29=0

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


Simplifying
y2 + -13y + 29 = 0

Reorder the terms:
29 + -13y + y2 = 0

Solving
29 + -13y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -13y + -29 + y2 = 0 + -29

Reorder the terms:
29 + -29 + -13y + y2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -13y + y2 = 0 + -29
-13y + y2 = 0 + -29

Combine like terms: 0 + -29 = -29
-13y + y2 = -29

The y term is -13y.  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.
-13y + 42.25 + y2 = -29 + 42.25

Reorder the terms:
42.25 + -13y + y2 = -29 + 42.25

Combine like terms: -29 + 42.25 = 13.25
42.25 + -13y + y2 = 13.25

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

Calculate the square root of the right side: 3.640054945

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


Subproblem 1
y + -6.5 = 3.640054945

Simplifying
y + -6.5 = 3.640054945

Reorder the terms:
-6.5 + y = 3.640054945

Solving
-6.5 + y = 3.640054945

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = 3.640054945 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = 3.640054945 + 6.5
y = 3.640054945 + 6.5

Combine like terms: 3.640054945 + 6.5 = 10.140054945
y = 10.140054945

Simplifying
y = 10.140054945


Subproblem 2
y + -6.5 = -3.640054945

Simplifying
y + -6.5 = -3.640054945

Reorder the terms:
-6.5 + y = -3.640054945

Solving
-6.5 + y = -3.640054945

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = -3.640054945 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = -3.640054945 + 6.5
y = -3.640054945 + 6.5

Combine like terms: -3.640054945 + 6.5 = 2.859945055
y = 2.859945055

Simplifying
y = 2.859945055


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

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