8=0.005y^2-0.01y

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Solution for 8=0.005y^2-0.01y equation:


Simplifying
8 = 0.005y2 + -0.01y

Reorder the terms:
8 = -0.01y + 0.005y2

Solving
8 = -0.01y + 0.005y2

Solving for variable 'y'.

Reorder the terms:
8 + 0.01y + -0.005y2 = -0.01y + 0.01y + 0.005y2 + -0.005y2

Combine like terms: -0.01y + 0.01y = 0.00
8 + 0.01y + -0.005y2 = 0.00 + 0.005y2 + -0.005y2
8 + 0.01y + -0.005y2 = 0.005y2 + -0.005y2

Combine like terms: 0.005y2 + -0.005y2 = 0.000
8 + 0.01y + -0.005y2 = 0.000

Begin completing the square.  Divide all terms by
-0.005 the coefficient of the squared term: 

Divide each side by '-0.005'.
-1600 + -2y + y2 = 0

Move the constant term to the right:

Add '1600' to each side of the equation.
-1600 + -2y + 1600 + y2 = 0 + 1600

Reorder the terms:
-1600 + 1600 + -2y + y2 = 0 + 1600

Combine like terms: -1600 + 1600 = 0
0 + -2y + y2 = 0 + 1600
-2y + y2 = 0 + 1600

Combine like terms: 0 + 1600 = 1600
-2y + y2 = 1600

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 1600 + 1

Reorder the terms:
1 + -2y + y2 = 1600 + 1

Combine like terms: 1600 + 1 = 1601
1 + -2y + y2 = 1601

Factor a perfect square on the left side:
(y + -1)(y + -1) = 1601

Calculate the square root of the right side: 40.012498047

Break this problem into two subproblems by setting 
(y + -1) equal to 40.012498047 and -40.012498047.

Subproblem 1

y + -1 = 40.012498047 Simplifying y + -1 = 40.012498047 Reorder the terms: -1 + y = 40.012498047 Solving -1 + y = 40.012498047 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 40.012498047 + 1 Combine like terms: -1 + 1 = 0 0 + y = 40.012498047 + 1 y = 40.012498047 + 1 Combine like terms: 40.012498047 + 1 = 41.012498047 y = 41.012498047 Simplifying y = 41.012498047

Subproblem 2

y + -1 = -40.012498047 Simplifying y + -1 = -40.012498047 Reorder the terms: -1 + y = -40.012498047 Solving -1 + y = -40.012498047 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -40.012498047 + 1 Combine like terms: -1 + 1 = 0 0 + y = -40.012498047 + 1 y = -40.012498047 + 1 Combine like terms: -40.012498047 + 1 = -39.012498047 y = -39.012498047 Simplifying y = -39.012498047

Solution

The solution to the problem is based on the solutions from the subproblems. y = {41.012498047, -39.012498047}

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