4y^2+40y+40y+25=0

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Solution for 4y^2+40y+40y+25=0 equation: 


Simplifying
4y2 + 40y + 40y + 25 = 0

Reorder the terms:
25 + 40y + 40y + 4y2 = 0

Combine like terms: 40y + 40y = 80y
25 + 80y + 4y2 = 0

Solving
25 + 80y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
6.25 + 20y + y2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 20y + -6.25 + y2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 20y + y2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 20y + y2 = 0 + -6.25
20y + y2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
20y + y2 = -6.25

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 = -6.25 + 100

Reorder the terms:
100 + 20y + y2 = -6.25 + 100

Combine like terms: -6.25 + 100 = 93.75
100 + 20y + y2 = 93.75

Factor a perfect square on the left side:
(y + 10)(y + 10) = 93.75

Calculate the square root of the right side: 9.682458366

Break this problem into two subproblems by setting 
(y + 10) equal to 9.682458366 and -9.682458366.


Subproblem 1
y + 10 = 9.682458366

Simplifying
y + 10 = 9.682458366

Reorder the terms:
10 + y = 9.682458366

Solving
10 + y = 9.682458366

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 = 9.682458366 + -10

Combine like terms: 10 + -10 = 0
0 + y = 9.682458366 + -10
y = 9.682458366 + -10

Combine like terms: 9.682458366 + -10 = -0.317541634
y = -0.317541634

Simplifying
y = -0.317541634


Subproblem 2
y + 10 = -9.682458366

Simplifying
y + 10 = -9.682458366

Reorder the terms:
10 + y = -9.682458366

Solving
10 + y = -9.682458366

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 = -9.682458366 + -10

Combine like terms: 10 + -10 = 0
0 + y = -9.682458366 + -10
y = -9.682458366 + -10

Combine like terms: -9.682458366 + -10 = -19.682458366
y = -19.682458366

Simplifying
y = -19.682458366


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.317541634, -19.682458366}

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