2y^2+10y+7=0

Solution for 2y^2+10y+7=0 equation:

Simplifying
2y2 + 10y + 7 = 0

Reorder the terms:
7 + 10y + 2y2 = 0

Solving
7 + 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'.
3.5 + 5y + y2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 5y + -3.5 + y2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 5y + y2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 5y + y2 = 0 + -3.5
5y + y2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
5y + y2 = -3.5

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 = -3.5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = -3.5 + 6.25

Combine like terms: -3.5 + 6.25 = 2.75
6.25 + 5y + y2 = 2.75

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + 2.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
y + 2.5 = 1.658312395

Simplifying
y + 2.5 = 1.658312395

Reorder the terms:
2.5 + y = 1.658312395

Solving
2.5 + y = 1.658312395

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 = 1.658312395 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 1.658312395 + -2.5
y = 1.658312395 + -2.5

Combine like terms: 1.658312395 + -2.5 = -0.841687605
y = -0.841687605

Simplifying
y = -0.841687605

Subproblem 2
y + 2.5 = -1.658312395

Simplifying
y + 2.5 = -1.658312395

Reorder the terms:
2.5 + y = -1.658312395

Solving
2.5 + y = -1.658312395

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 = -1.658312395 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -1.658312395 + -2.5
y = -1.658312395 + -2.5

Combine like terms: -1.658312395 + -2.5 = -4.158312395
y = -4.158312395

Simplifying
y = -4.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.841687605, -4.158312395}