y^2-20y-270=0

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Solution for y^2-20y-270=0 equation: 


Simplifying
y2 + -20y + -270 = 0

Reorder the terms:
-270 + -20y + y2 = 0

Solving
-270 + -20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '270' to each side of the equation.
-270 + -20y + 270 + y2 = 0 + 270

Reorder the terms:
-270 + 270 + -20y + y2 = 0 + 270

Combine like terms: -270 + 270 = 0
0 + -20y + y2 = 0 + 270
-20y + y2 = 0 + 270

Combine like terms: 0 + 270 = 270
-20y + y2 = 270

The y term is -20y.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20y + 100 + y2 = 270 + 100

Reorder the terms:
100 + -20y + y2 = 270 + 100

Combine like terms: 270 + 100 = 370
100 + -20y + y2 = 370

Factor a perfect square on the left side:
(y + -10)(y + -10) = 370

Calculate the square root of the right side: 19.235384062

Break this problem into two subproblems by setting 
(y + -10) equal to 19.235384062 and -19.235384062.


Subproblem 1
y + -10 = 19.235384062

Simplifying
y + -10 = 19.235384062

Reorder the terms:
-10 + y = 19.235384062

Solving
-10 + y = 19.235384062

Solving for variable 'y'.

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

Add '10' to each side of the equation.
-10 + 10 + y = 19.235384062 + 10

Combine like terms: -10 + 10 = 0
0 + y = 19.235384062 + 10
y = 19.235384062 + 10

Combine like terms: 19.235384062 + 10 = 29.235384062
y = 29.235384062

Simplifying
y = 29.235384062


Subproblem 2
y + -10 = -19.235384062

Simplifying
y + -10 = -19.235384062

Reorder the terms:
-10 + y = -19.235384062

Solving
-10 + y = -19.235384062

Solving for variable 'y'.

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

Add '10' to each side of the equation.
-10 + 10 + y = -19.235384062 + 10

Combine like terms: -10 + 10 = 0
0 + y = -19.235384062 + 10
y = -19.235384062 + 10

Combine like terms: -19.235384062 + 10 = -9.235384062
y = -9.235384062

Simplifying
y = -9.235384062


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {29.235384062, -9.235384062}

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