y^2+51y-270.75=0

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Solution for y^2+51y-270.75=0 equation: 


Simplifying
y2 + 51y + -270.75 = 0

Reorder the terms:
-270.75 + 51y + y2 = 0

Solving
-270.75 + 51y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '270.75' to each side of the equation.
-270.75 + 51y + 270.75 + y2 = 0 + 270.75

Reorder the terms:
-270.75 + 270.75 + 51y + y2 = 0 + 270.75

Combine like terms: -270.75 + 270.75 = 0.00
0.00 + 51y + y2 = 0 + 270.75
51y + y2 = 0 + 270.75

Combine like terms: 0 + 270.75 = 270.75
51y + y2 = 270.75

The y term is 51y.  Take half its coefficient (25.5).
Square it (650.25) and add it to both sides.

Add '650.25' to each side of the equation.
51y + 650.25 + y2 = 270.75 + 650.25

Reorder the terms:
650.25 + 51y + y2 = 270.75 + 650.25

Combine like terms: 270.75 + 650.25 = 921
650.25 + 51y + y2 = 921

Factor a perfect square on the left side:
(y + 25.5)(y + 25.5) = 921

Calculate the square root of the right side: 30.347981811

Break this problem into two subproblems by setting 
(y + 25.5) equal to 30.347981811 and -30.347981811.


Subproblem 1
y + 25.5 = 30.347981811

Simplifying
y + 25.5 = 30.347981811

Reorder the terms:
25.5 + y = 30.347981811

Solving
25.5 + y = 30.347981811

Solving for variable 'y'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + y = 30.347981811 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + y = 30.347981811 + -25.5
y = 30.347981811 + -25.5

Combine like terms: 30.347981811 + -25.5 = 4.847981811
y = 4.847981811

Simplifying
y = 4.847981811


Subproblem 2
y + 25.5 = -30.347981811

Simplifying
y + 25.5 = -30.347981811

Reorder the terms:
25.5 + y = -30.347981811

Solving
25.5 + y = -30.347981811

Solving for variable 'y'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + y = -30.347981811 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + y = -30.347981811 + -25.5
y = -30.347981811 + -25.5

Combine like terms: -30.347981811 + -25.5 = -55.847981811
y = -55.847981811

Simplifying
y = -55.847981811


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.847981811, -55.847981811}

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