2y^2+10y-801=0

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Solution for 2y^2+10y-801=0 equation: 


Simplifying
2y2 + 10y + -801 = 0

Reorder the terms:
-801 + 10y + 2y2 = 0

Solving
-801 + 10y + 2y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-400.5 + 5y + y2 = 0

Move the constant term to the right:

Add '400.5' to each side of the equation.
-400.5 + 5y + 400.5 + y2 = 0 + 400.5

Reorder the terms:
-400.5 + 400.5 + 5y + y2 = 0 + 400.5

Combine like terms: -400.5 + 400.5 = 0.0
0.0 + 5y + y2 = 0 + 400.5
5y + y2 = 0 + 400.5

Combine like terms: 0 + 400.5 = 400.5
5y + y2 = 400.5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 400.5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 400.5 + 6.25

Combine like terms: 400.5 + 6.25 = 406.75
6.25 + 5y + y2 = 406.75

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 406.75

Calculate the square root of the right side: 20.16804403

Break this problem into two subproblems by setting 
(y + 2.5) equal to 20.16804403 and -20.16804403.


Subproblem 1
y + 2.5 = 20.16804403

Simplifying
y + 2.5 = 20.16804403

Reorder the terms:
2.5 + y = 20.16804403

Solving
2.5 + y = 20.16804403

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 20.16804403 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 20.16804403 + -2.5
y = 20.16804403 + -2.5

Combine like terms: 20.16804403 + -2.5 = 17.66804403
y = 17.66804403

Simplifying
y = 17.66804403


Subproblem 2
y + 2.5 = -20.16804403

Simplifying
y + 2.5 = -20.16804403

Reorder the terms:
2.5 + y = -20.16804403

Solving
2.5 + y = -20.16804403

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -20.16804403 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -20.16804403 + -2.5
y = -20.16804403 + -2.5

Combine like terms: -20.16804403 + -2.5 = -22.66804403
y = -22.66804403

Simplifying
y = -22.66804403


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.66804403, -22.66804403}

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