y^2+51y-157.9375=0

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Solution for y^2+51y-157.9375=0 equation: 


Simplifying
y2 + 51y + -157.9375 = 0

Reorder the terms:
-157.9375 + 51y + y2 = 0

Solving
-157.9375 + 51y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '157.9375' to each side of the equation.
-157.9375 + 51y + 157.9375 + y2 = 0 + 157.9375

Reorder the terms:
-157.9375 + 157.9375 + 51y + y2 = 0 + 157.9375

Combine like terms: -157.9375 + 157.9375 = 0.0000
0.0000 + 51y + y2 = 0 + 157.9375
51y + y2 = 0 + 157.9375

Combine like terms: 0 + 157.9375 = 157.9375
51y + y2 = 157.9375

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 = 157.9375 + 650.25

Reorder the terms:
650.25 + 51y + y2 = 157.9375 + 650.25

Combine like terms: 157.9375 + 650.25 = 808.1875
650.25 + 51y + y2 = 808.1875

Factor a perfect square on the left side:
(y + 25.5)(y + 25.5) = 808.1875

Calculate the square root of the right side: 28.428638729

Break this problem into two subproblems by setting 
(y + 25.5) equal to 28.428638729 and -28.428638729.


Subproblem 1
y + 25.5 = 28.428638729

Simplifying
y + 25.5 = 28.428638729

Reorder the terms:
25.5 + y = 28.428638729

Solving
25.5 + y = 28.428638729

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 = 28.428638729 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + y = 28.428638729 + -25.5
y = 28.428638729 + -25.5

Combine like terms: 28.428638729 + -25.5 = 2.928638729
y = 2.928638729

Simplifying
y = 2.928638729


Subproblem 2
y + 25.5 = -28.428638729

Simplifying
y + 25.5 = -28.428638729

Reorder the terms:
25.5 + y = -28.428638729

Solving
25.5 + y = -28.428638729

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 = -28.428638729 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + y = -28.428638729 + -25.5
y = -28.428638729 + -25.5

Combine like terms: -28.428638729 + -25.5 = -53.928638729
y = -53.928638729

Simplifying
y = -53.928638729


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.928638729, -53.928638729}

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