y^2+18y-194=0

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Solution for y^2+18y-194=0 equation: 


Simplifying
y2 + 18y + -194 = 0

Reorder the terms:
-194 + 18y + y2 = 0

Solving
-194 + 18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '194' to each side of the equation.
-194 + 18y + 194 + y2 = 0 + 194

Reorder the terms:
-194 + 194 + 18y + y2 = 0 + 194

Combine like terms: -194 + 194 = 0
0 + 18y + y2 = 0 + 194
18y + y2 = 0 + 194

Combine like terms: 0 + 194 = 194
18y + y2 = 194

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 = 194 + 81

Reorder the terms:
81 + 18y + y2 = 194 + 81

Combine like terms: 194 + 81 = 275
81 + 18y + y2 = 275

Factor a perfect square on the left side:
(y + 9)(y + 9) = 275

Calculate the square root of the right side: 16.583123952

Break this problem into two subproblems by setting 
(y + 9) equal to 16.583123952 and -16.583123952.


Subproblem 1
y + 9 = 16.583123952

Simplifying
y + 9 = 16.583123952

Reorder the terms:
9 + y = 16.583123952

Solving
9 + y = 16.583123952

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 = 16.583123952 + -9

Combine like terms: 9 + -9 = 0
0 + y = 16.583123952 + -9
y = 16.583123952 + -9

Combine like terms: 16.583123952 + -9 = 7.583123952
y = 7.583123952

Simplifying
y = 7.583123952


Subproblem 2
y + 9 = -16.583123952

Simplifying
y + 9 = -16.583123952

Reorder the terms:
9 + y = -16.583123952

Solving
9 + y = -16.583123952

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 = -16.583123952 + -9

Combine like terms: 9 + -9 = 0
0 + y = -16.583123952 + -9
y = -16.583123952 + -9

Combine like terms: -16.583123952 + -9 = -25.583123952
y = -25.583123952

Simplifying
y = -25.583123952


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.583123952, -25.583123952}

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