(y+0.01)y=0.0000257

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Solution for (y+0.01)y=0.0000257 equation: 


Simplifying
(y + 0.01) * y = 0.0000257

Reorder the terms:
(0.01 + y) * y = 0.0000257

Reorder the terms for easier multiplication:
y(0.01 + y) = 0.0000257
(0.01 * y + y * y) = 0.0000257
(0.01y + y2) = 0.0000257

Solving
0.01y + y2 = 0.0000257

Solving for variable 'y'.

Reorder the terms:
-0.0000257 + 0.01y + y2 = 0.0000257 + -0.0000257

Combine like terms: 0.0000257 + -0.0000257 = 0.0000000
-0.0000257 + 0.01y + y2 = 0.0000000

Begin completing the square.

Move the constant term to the right:

Add '0.0000257' to each side of the equation.
-0.0000257 + 0.01y + 0.0000257 + y2 = 0.0000000 + 0.0000257

Reorder the terms:
-0.0000257 + 0.0000257 + 0.01y + y2 = 0.0000000 + 0.0000257

Combine like terms: -0.0000257 + 0.0000257 = 0.0000000
0.0000000 + 0.01y + y2 = 0.0000000 + 0.0000257
0.01y + y2 = 0.0000000 + 0.0000257

Combine like terms: 0.0000000 + 0.0000257 = 0.0000257
0.01y + y2 = 0.0000257

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 = 0.0000257 + 0.000025

Reorder the terms:
0.000025 + 0.01y + y2 = 0.0000257 + 0.000025

Combine like terms: 0.0000257 + 0.000025 = 0.0000507
0.000025 + 0.01y + y2 = 0.0000507

Factor a perfect square on the left side:
(y + 0.005)(y + 0.005) = 0.0000507

Calculate the square root of the right side: 0.007120393

Break this problem into two subproblems by setting 
(y + 0.005) equal to 0.007120393 and -0.007120393.


Subproblem 1
y + 0.005 = 0.007120393

Simplifying
y + 0.005 = 0.007120393

Reorder the terms:
0.005 + y = 0.007120393

Solving
0.005 + y = 0.007120393

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 = 0.007120393 + -0.005

Combine like terms: 0.005 + -0.005 = 0.000
0.000 + y = 0.007120393 + -0.005
y = 0.007120393 + -0.005

Combine like terms: 0.007120393 + -0.005 = 0.002120393
y = 0.002120393

Simplifying
y = 0.002120393


Subproblem 2
y + 0.005 = -0.007120393

Simplifying
y + 0.005 = -0.007120393

Reorder the terms:
0.005 + y = -0.007120393

Solving
0.005 + y = -0.007120393

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 = -0.007120393 + -0.005

Combine like terms: 0.005 + -0.005 = 0.000
0.000 + y = -0.007120393 + -0.005
y = -0.007120393 + -0.005

Combine like terms: -0.007120393 + -0.005 = -0.012120393
y = -0.012120393

Simplifying
y = -0.012120393


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.002120393, -0.012120393}

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