5*y*y+16*y+13=100

Solution for 5*y*y+16*y+13=100 equation:

Simplifying
5y * y + 16y + 13 = 100

Multiply y * y
5y2 + 16y + 13 = 100

Reorder the terms:
13 + 16y + 5y2 = 100

Solving
13 + 16y + 5y2 = 100

Solving for variable 'y'.

Reorder the terms:
13 + -100 + 16y + 5y2 = 100 + -100

Combine like terms: 13 + -100 = -87
-87 + 16y + 5y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-87 + 16y + 5y2 = 0

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

Divide each side by '5'.
-17.4 + 3.2y + y2 = 0

Move the constant term to the right:

Add '17.4' to each side of the equation.
-17.4 + 3.2y + 17.4 + y2 = 0 + 17.4

Reorder the terms:
-17.4 + 17.4 + 3.2y + y2 = 0 + 17.4

Combine like terms: -17.4 + 17.4 = 0.0
0.0 + 3.2y + y2 = 0 + 17.4
3.2y + y2 = 0 + 17.4

Combine like terms: 0 + 17.4 = 17.4
3.2y + y2 = 17.4

The y term is 3.2y.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2y + 2.56 + y2 = 17.4 + 2.56

Reorder the terms:
2.56 + 3.2y + y2 = 17.4 + 2.56

Combine like terms: 17.4 + 2.56 = 19.96
2.56 + 3.2y + y2 = 19.96

Factor a perfect square on the left side:
(y + 1.6)(y + 1.6) = 19.96

Calculate the square root of the right side: 4.467661581

Break this problem into two subproblems by setting 
(y + 1.6) equal to 4.467661581 and -4.467661581.

Subproblem 1
y + 1.6 = 4.467661581

Simplifying
y + 1.6 = 4.467661581

Reorder the terms:
1.6 + y = 4.467661581

Solving
1.6 + y = 4.467661581

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = 4.467661581 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = 4.467661581 + -1.6
y = 4.467661581 + -1.6

Combine like terms: 4.467661581 + -1.6 = 2.867661581
y = 2.867661581

Simplifying
y = 2.867661581

Subproblem 2
y + 1.6 = -4.467661581

Simplifying
y + 1.6 = -4.467661581

Reorder the terms:
1.6 + y = -4.467661581

Solving
1.6 + y = -4.467661581

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = -4.467661581 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = -4.467661581 + -1.6
y = -4.467661581 + -1.6

Combine like terms: -4.467661581 + -1.6 = -6.067661581
y = -6.067661581

Simplifying
y = -6.067661581

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.867661581, -6.067661581}