100y^2-5y-2=0

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Solution for 100y^2-5y-2=0 equation: 


Simplifying
100y2 + -5y + -2 = 0

Reorder the terms:
-2 + -5y + 100y2 = 0

Solving
-2 + -5y + 100y2 = 0

Solving for variable 'y'.

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

Divide each side by '100'.
-0.02 + -0.05y + y2 = 0

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + -0.05y + 0.02 + y2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + -0.05y + y2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + -0.05y + y2 = 0 + 0.02
-0.05y + y2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
-0.05y + y2 = 0.02

The y term is -0.05y.  Take half its coefficient (-0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
-0.05y + 0.000625 + y2 = 0.02 + 0.000625

Reorder the terms:
0.000625 + -0.05y + y2 = 0.02 + 0.000625

Combine like terms: 0.02 + 0.000625 = 0.020625
0.000625 + -0.05y + y2 = 0.020625

Factor a perfect square on the left side:
(y + -0.025)(y + -0.025) = 0.020625

Calculate the square root of the right side: 0.143614066

Break this problem into two subproblems by setting 
(y + -0.025) equal to 0.143614066 and -0.143614066.


Subproblem 1
y + -0.025 = 0.143614066

Simplifying
y + -0.025 = 0.143614066

Reorder the terms:
-0.025 + y = 0.143614066

Solving
-0.025 + y = 0.143614066

Solving for variable 'y'.

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

Add '0.025' to each side of the equation.
-0.025 + 0.025 + y = 0.143614066 + 0.025

Combine like terms: -0.025 + 0.025 = 0.000
0.000 + y = 0.143614066 + 0.025
y = 0.143614066 + 0.025

Combine like terms: 0.143614066 + 0.025 = 0.168614066
y = 0.168614066

Simplifying
y = 0.168614066


Subproblem 2
y + -0.025 = -0.143614066

Simplifying
y + -0.025 = -0.143614066

Reorder the terms:
-0.025 + y = -0.143614066

Solving
-0.025 + y = -0.143614066

Solving for variable 'y'.

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

Add '0.025' to each side of the equation.
-0.025 + 0.025 + y = -0.143614066 + 0.025

Combine like terms: -0.025 + 0.025 = 0.000
0.000 + y = -0.143614066 + 0.025
y = -0.143614066 + 0.025

Combine like terms: -0.143614066 + 0.025 = -0.118614066
y = -0.118614066

Simplifying
y = -0.118614066


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.168614066, -0.118614066}

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