y^2-26y-9=0

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Solution for y^2-26y-9=0 equation: 


Simplifying
y2 + -26y + -9 = 0

Reorder the terms:
-9 + -26y + y2 = 0

Solving
-9 + -26y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -26y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + -26y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -26y + y2 = 0 + 9
-26y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-26y + y2 = 9

The y term is -26y.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26y + 169 + y2 = 9 + 169

Reorder the terms:
169 + -26y + y2 = 9 + 169

Combine like terms: 9 + 169 = 178
169 + -26y + y2 = 178

Factor a perfect square on the left side:
(y + -13)(y + -13) = 178

Calculate the square root of the right side: 13.341664064

Break this problem into two subproblems by setting 
(y + -13) equal to 13.341664064 and -13.341664064.


Subproblem 1
y + -13 = 13.341664064

Simplifying
y + -13 = 13.341664064

Reorder the terms:
-13 + y = 13.341664064

Solving
-13 + y = 13.341664064

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = 13.341664064 + 13

Combine like terms: -13 + 13 = 0
0 + y = 13.341664064 + 13
y = 13.341664064 + 13

Combine like terms: 13.341664064 + 13 = 26.341664064
y = 26.341664064

Simplifying
y = 26.341664064


Subproblem 2
y + -13 = -13.341664064

Simplifying
y + -13 = -13.341664064

Reorder the terms:
-13 + y = -13.341664064

Solving
-13 + y = -13.341664064

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = -13.341664064 + 13

Combine like terms: -13 + 13 = 0
0 + y = -13.341664064 + 13
y = -13.341664064 + 13

Combine like terms: -13.341664064 + 13 = -0.341664064
y = -0.341664064

Simplifying
y = -0.341664064


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {26.341664064, -0.341664064}

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