y^2-18y+26=0

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Solution for y^2-18y+26=0 equation: 


Simplifying
y2 + -18y + 26 = 0

Reorder the terms:
26 + -18y + y2 = 0

Solving
26 + -18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -18y + -26 + y2 = 0 + -26

Reorder the terms:
26 + -26 + -18y + y2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -18y + y2 = 0 + -26
-18y + y2 = 0 + -26

Combine like terms: 0 + -26 = -26
-18y + y2 = -26

The y term is -18y.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18y + 81 + y2 = -26 + 81

Reorder the terms:
81 + -18y + y2 = -26 + 81

Combine like terms: -26 + 81 = 55
81 + -18y + y2 = 55

Factor a perfect square on the left side:
(y + -9)(y + -9) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(y + -9) equal to 7.416198487 and -7.416198487.


Subproblem 1
y + -9 = 7.416198487

Simplifying
y + -9 = 7.416198487

Reorder the terms:
-9 + y = 7.416198487

Solving
-9 + y = 7.416198487

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = 7.416198487 + 9

Combine like terms: -9 + 9 = 0
0 + y = 7.416198487 + 9
y = 7.416198487 + 9

Combine like terms: 7.416198487 + 9 = 16.416198487
y = 16.416198487

Simplifying
y = 16.416198487


Subproblem 2
y + -9 = -7.416198487

Simplifying
y + -9 = -7.416198487

Reorder the terms:
-9 + y = -7.416198487

Solving
-9 + y = -7.416198487

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = -7.416198487 + 9

Combine like terms: -9 + 9 = 0
0 + y = -7.416198487 + 9
y = -7.416198487 + 9

Combine like terms: -7.416198487 + 9 = 1.583801513
y = 1.583801513

Simplifying
y = 1.583801513


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.416198487, 1.583801513}

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