100y^2+72y-4=0

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Solution for 100y^2+72y-4=0 equation: 


Simplifying
100y2 + 72y + -4 = 0

Reorder the terms:
-4 + 72y + 100y2 = 0

Solving
-4 + 72y + 100y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 18y + 25y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 18y + 25y2)' equal to zero and attempt to solve:

Simplifying
-1 + 18y + 25y2 = 0

Solving
-1 + 18y + 25y2 = 0

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

Divide each side by '25'.
-0.04 + 0.72y + y2 = 0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.72y + 0.04 + y2 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.72y + y2 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.72y + y2 = 0 + 0.04
0.72y + y2 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.72y + y2 = 0.04

The y term is 0.72y.  Take half its coefficient (0.36).
Square it (0.1296) and add it to both sides.

Add '0.1296' to each side of the equation.
0.72y + 0.1296 + y2 = 0.04 + 0.1296

Reorder the terms:
0.1296 + 0.72y + y2 = 0.04 + 0.1296

Combine like terms: 0.04 + 0.1296 = 0.1696
0.1296 + 0.72y + y2 = 0.1696

Factor a perfect square on the left side:
(y + 0.36)(y + 0.36) = 0.1696

Calculate the square root of the right side: 0.411825206

Break this problem into two subproblems by setting 
(y + 0.36) equal to 0.411825206 and -0.411825206.


Subproblem 1
y + 0.36 = 0.411825206

Simplifying
y + 0.36 = 0.411825206

Reorder the terms:
0.36 + y = 0.411825206

Solving
0.36 + y = 0.411825206

Solving for variable 'y'.

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

Add '-0.36' to each side of the equation.
0.36 + -0.36 + y = 0.411825206 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + y = 0.411825206 + -0.36
y = 0.411825206 + -0.36

Combine like terms: 0.411825206 + -0.36 = 0.051825206
y = 0.051825206

Simplifying
y = 0.051825206


Subproblem 2
y + 0.36 = -0.411825206

Simplifying
y + 0.36 = -0.411825206

Reorder the terms:
0.36 + y = -0.411825206

Solving
0.36 + y = -0.411825206

Solving for variable 'y'.

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

Add '-0.36' to each side of the equation.
0.36 + -0.36 + y = -0.411825206 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + y = -0.411825206 + -0.36
y = -0.411825206 + -0.36

Combine like terms: -0.411825206 + -0.36 = -0.771825206
y = -0.771825206

Simplifying
y = -0.771825206


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.051825206, -0.771825206}
Solution
y = {0.051825206, -0.771825206}

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