(y+0.01)y=5

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Solution for (y+0.01)y=5 equation: 


Simplifying
(y + 0.01) * y = 5

Reorder the terms:
(0.01 + y) * y = 5

Reorder the terms for easier multiplication:
y(0.01 + y) = 5
(0.01 * y + y * y) = 5
(0.01y + y2) = 5

Solving
0.01y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 0.01y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 0.01y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.01y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 0.01y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.01y + y2 = 0 + 5
0.01y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
0.01y + y2 = 5

The y term is 0.01y.  Take half its coefficient (0.005).
Square it (0.000025) and add it to both sides.

Add '0.000025' to each side of the equation.
0.01y + 0.000025 + y2 = 5 + 0.000025

Reorder the terms:
0.000025 + 0.01y + y2 = 5 + 0.000025

Combine like terms: 5 + 0.000025 = 5.000025
0.000025 + 0.01y + y2 = 5.000025

Factor a perfect square on the left side:
(y + 0.005)(y + 0.005) = 5.000025

Calculate the square root of the right side: 2.236073568

Break this problem into two subproblems by setting 
(y + 0.005) equal to 2.236073568 and -2.236073568.


Subproblem 1
y + 0.005 = 2.236073568

Simplifying
y + 0.005 = 2.236073568

Reorder the terms:
0.005 + y = 2.236073568

Solving
0.005 + y = 2.236073568

Solving for variable 'y'.

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

Add '-0.005' to each side of the equation.
0.005 + -0.005 + y = 2.236073568 + -0.005

Combine like terms: 0.005 + -0.005 = 0.000
0.000 + y = 2.236073568 + -0.005
y = 2.236073568 + -0.005

Combine like terms: 2.236073568 + -0.005 = 2.231073568
y = 2.231073568

Simplifying
y = 2.231073568


Subproblem 2
y + 0.005 = -2.236073568

Simplifying
y + 0.005 = -2.236073568

Reorder the terms:
0.005 + y = -2.236073568

Solving
0.005 + y = -2.236073568

Solving for variable 'y'.

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

Add '-0.005' to each side of the equation.
0.005 + -0.005 + y = -2.236073568 + -0.005

Combine like terms: 0.005 + -0.005 = 0.000
0.000 + y = -2.236073568 + -0.005
y = -2.236073568 + -0.005

Combine like terms: -2.236073568 + -0.005 = -2.241073568
y = -2.241073568

Simplifying
y = -2.241073568


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.231073568, -2.241073568}

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