(0.7-y)*y=0.008

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Solution for (0.7-y)*y=0.008 equation: 


Simplifying
(0.7 + -1y) * y = 0.008

Reorder the terms for easier multiplication:
y(0.7 + -1y) = 0.008
(0.7 * y + -1y * y) = 0.008
(0.7y + -1y2) = 0.008

Solving
0.7y + -1y2 = 0.008

Solving for variable 'y'.

Reorder the terms:
-0.008 + 0.7y + -1y2 = 0.008 + -0.008

Combine like terms: 0.008 + -0.008 = 0.000
-0.008 + 0.7y + -1y2 = 0.000

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.008 + -0.7y + y2 = 0.000

Move the constant term to the right:

Add '-0.008' to each side of the equation.
0.008 + -0.7y + -0.008 + y2 = 0.000 + -0.008

Reorder the terms:
0.008 + -0.008 + -0.7y + y2 = 0.000 + -0.008

Combine like terms: 0.008 + -0.008 = 0.000
0.000 + -0.7y + y2 = 0.000 + -0.008
-0.7y + y2 = 0.000 + -0.008

Combine like terms: 0.000 + -0.008 = -0.008
-0.7y + y2 = -0.008

The y term is -0.7y.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7y + 0.1225 + y2 = -0.008 + 0.1225

Reorder the terms:
0.1225 + -0.7y + y2 = -0.008 + 0.1225

Combine like terms: -0.008 + 0.1225 = 0.1145
0.1225 + -0.7y + y2 = 0.1145

Factor a perfect square on the left side:
(y + -0.35)(y + -0.35) = 0.1145

Calculate the square root of the right side: 0.338378486

Break this problem into two subproblems by setting 
(y + -0.35) equal to 0.338378486 and -0.338378486.


Subproblem 1
y + -0.35 = 0.338378486

Simplifying
y + -0.35 = 0.338378486

Reorder the terms:
-0.35 + y = 0.338378486

Solving
-0.35 + y = 0.338378486

Solving for variable 'y'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + y = 0.338378486 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + y = 0.338378486 + 0.35
y = 0.338378486 + 0.35

Combine like terms: 0.338378486 + 0.35 = 0.688378486
y = 0.688378486

Simplifying
y = 0.688378486


Subproblem 2
y + -0.35 = -0.338378486

Simplifying
y + -0.35 = -0.338378486

Reorder the terms:
-0.35 + y = -0.338378486

Solving
-0.35 + y = -0.338378486

Solving for variable 'y'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + y = -0.338378486 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + y = -0.338378486 + 0.35
y = -0.338378486 + 0.35

Combine like terms: -0.338378486 + 0.35 = 0.011621514
y = 0.011621514

Simplifying
y = 0.011621514


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.688378486, 0.011621514}

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