4y^2+28y-802=0

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Solution for 4y^2+28y-802=0 equation: 


Simplifying
4y2 + 28y + -802 = 0

Reorder the terms:
-802 + 28y + 4y2 = 0

Solving
-802 + 28y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-401 + 14y + 2y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-401 + 14y + 2y2)' equal to zero and attempt to solve:

Simplifying
-401 + 14y + 2y2 = 0

Solving
-401 + 14y + 2y2 = 0

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

Divide each side by '2'.
-200.5 + 7y + y2 = 0

Move the constant term to the right:

Add '200.5' to each side of the equation.
-200.5 + 7y + 200.5 + y2 = 0 + 200.5

Reorder the terms:
-200.5 + 200.5 + 7y + y2 = 0 + 200.5

Combine like terms: -200.5 + 200.5 = 0.0
0.0 + 7y + y2 = 0 + 200.5
7y + y2 = 0 + 200.5

Combine like terms: 0 + 200.5 = 200.5
7y + y2 = 200.5

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = 200.5 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 200.5 + 12.25

Combine like terms: 200.5 + 12.25 = 212.75
12.25 + 7y + y2 = 212.75

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 212.75

Calculate the square root of the right side: 14.585952146

Break this problem into two subproblems by setting 
(y + 3.5) equal to 14.585952146 and -14.585952146.


Subproblem 1
y + 3.5 = 14.585952146

Simplifying
y + 3.5 = 14.585952146

Reorder the terms:
3.5 + y = 14.585952146

Solving
3.5 + y = 14.585952146

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 14.585952146 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 14.585952146 + -3.5
y = 14.585952146 + -3.5

Combine like terms: 14.585952146 + -3.5 = 11.085952146
y = 11.085952146

Simplifying
y = 11.085952146


Subproblem 2
y + 3.5 = -14.585952146

Simplifying
y + 3.5 = -14.585952146

Reorder the terms:
3.5 + y = -14.585952146

Solving
3.5 + y = -14.585952146

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -14.585952146 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -14.585952146 + -3.5
y = -14.585952146 + -3.5

Combine like terms: -14.585952146 + -3.5 = -18.085952146
y = -18.085952146

Simplifying
y = -18.085952146


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.085952146, -18.085952146}
Solution
y = {11.085952146, -18.085952146}

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