y^2-22y-120=0

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Solution for y^2-22y-120=0 equation: 


Simplifying
y2 + -22y + -120 = 0

Reorder the terms:
-120 + -22y + y2 = 0

Solving
-120 + -22y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -22y + 120 + y2 = 0 + 120

Reorder the terms:
-120 + 120 + -22y + y2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -22y + y2 = 0 + 120
-22y + y2 = 0 + 120

Combine like terms: 0 + 120 = 120
-22y + y2 = 120

The y term is -22y.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22y + 121 + y2 = 120 + 121

Reorder the terms:
121 + -22y + y2 = 120 + 121

Combine like terms: 120 + 121 = 241
121 + -22y + y2 = 241

Factor a perfect square on the left side:
(y + -11)(y + -11) = 241

Calculate the square root of the right side: 15.524174696

Break this problem into two subproblems by setting 
(y + -11) equal to 15.524174696 and -15.524174696.


Subproblem 1
y + -11 = 15.524174696

Simplifying
y + -11 = 15.524174696

Reorder the terms:
-11 + y = 15.524174696

Solving
-11 + y = 15.524174696

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = 15.524174696 + 11

Combine like terms: -11 + 11 = 0
0 + y = 15.524174696 + 11
y = 15.524174696 + 11

Combine like terms: 15.524174696 + 11 = 26.524174696
y = 26.524174696

Simplifying
y = 26.524174696


Subproblem 2
y + -11 = -15.524174696

Simplifying
y + -11 = -15.524174696

Reorder the terms:
-11 + y = -15.524174696

Solving
-11 + y = -15.524174696

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = -15.524174696 + 11

Combine like terms: -11 + 11 = 0
0 + y = -15.524174696 + 11
y = -15.524174696 + 11

Combine like terms: -15.524174696 + 11 = -4.524174696
y = -4.524174696

Simplifying
y = -4.524174696


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {26.524174696, -4.524174696}

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