25y^2+50y+18=0

Solution for 25y^2+50y+18=0 equation:

Simplifying
25y2 + 50y + 18 = 0

Reorder the terms:
18 + 50y + 25y2 = 0

Solving
18 + 50y + 25y2 = 0

Solving for variable 'y'.

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

Divide each side by '25'.
0.72 + 2y + y2 = 0

Move the constant term to the right:

Add '-0.72' to each side of the equation.
0.72 + 2y + -0.72 + y2 = 0 + -0.72

Reorder the terms:
0.72 + -0.72 + 2y + y2 = 0 + -0.72

Combine like terms: 0.72 + -0.72 = 0.00
0.00 + 2y + y2 = 0 + -0.72
2y + y2 = 0 + -0.72

Combine like terms: 0 + -0.72 = -0.72
2y + y2 = -0.72

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -0.72 + 1

Reorder the terms:
1 + 2y + y2 = -0.72 + 1

Combine like terms: -0.72 + 1 = 0.28
1 + 2y + y2 = 0.28

Factor a perfect square on the left side:
(y + 1)(y + 1) = 0.28

Calculate the square root of the right side: 0.529150262

Break this problem into two subproblems by setting 
(y + 1) equal to 0.529150262 and -0.529150262.

Subproblem 1
y + 1 = 0.529150262

Simplifying
y + 1 = 0.529150262

Reorder the terms:
1 + y = 0.529150262

Solving
1 + y = 0.529150262

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 0.529150262 + -1

Combine like terms: 1 + -1 = 0
0 + y = 0.529150262 + -1
y = 0.529150262 + -1

Combine like terms: 0.529150262 + -1 = -0.470849738
y = -0.470849738

Simplifying
y = -0.470849738

Subproblem 2
y + 1 = -0.529150262

Simplifying
y + 1 = -0.529150262

Reorder the terms:
1 + y = -0.529150262

Solving
1 + y = -0.529150262

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -0.529150262 + -1

Combine like terms: 1 + -1 = 0
0 + y = -0.529150262 + -1
y = -0.529150262 + -1

Combine like terms: -0.529150262 + -1 = -1.529150262
y = -1.529150262

Simplifying
y = -1.529150262

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.470849738, -1.529150262}