0.12y+0.08y(y+5000)=1400

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Solution for 0.12y+0.08y(y+5000)=1400 equation:


Simplifying
0.12y + 0.08y(y + 5000) = 1400

Reorder the terms:
0.12y + 0.08y(5000 + y) = 1400
0.12y + (5000 * 0.08y + y * 0.08y) = 1400
0.12y + (400y + 0.08y2) = 1400

Combine like terms: 0.12y + 400y = 400.12y
400.12y + 0.08y2 = 1400

Solving
400.12y + 0.08y2 = 1400

Solving for variable 'y'.

Reorder the terms:
-1400 + 400.12y + 0.08y2 = 1400 + -1400

Combine like terms: 1400 + -1400 = 0
-1400 + 400.12y + 0.08y2 = 0

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

Divide each side by '0.08'.
-17500 + 5001.5y + y2 = 0

Move the constant term to the right:

Add '17500' to each side of the equation.
-17500 + 5001.5y + 17500 + y2 = 0 + 17500

Reorder the terms:
-17500 + 17500 + 5001.5y + y2 = 0 + 17500

Combine like terms: -17500 + 17500 = 0
0 + 5001.5y + y2 = 0 + 17500
5001.5y + y2 = 0 + 17500

Combine like terms: 0 + 17500 = 17500
5001.5y + y2 = 17500

The y term is 5001.5y.  Take half its coefficient (2500.75).
Square it (6253750.563) and add it to both sides.

Add '6253750.563' to each side of the equation.
5001.5y + 6253750.563 + y2 = 17500 + 6253750.563

Reorder the terms:
6253750.563 + 5001.5y + y2 = 17500 + 6253750.563

Combine like terms: 17500 + 6253750.563 = 6271250.563
6253750.563 + 5001.5y + y2 = 6271250.563

Factor a perfect square on the left side:
(y + 2500.75)(y + 2500.75) = 6271250.563

Calculate the square root of the right side: 2504.246506037

Break this problem into two subproblems by setting 
(y + 2500.75) equal to 2504.246506037 and -2504.246506037.

Subproblem 1

y + 2500.75 = 2504.246506037 Simplifying y + 2500.75 = 2504.246506037 Reorder the terms: 2500.75 + y = 2504.246506037 Solving 2500.75 + y = 2504.246506037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2500.75' to each side of the equation. 2500.75 + -2500.75 + y = 2504.246506037 + -2500.75 Combine like terms: 2500.75 + -2500.75 = 0.00 0.00 + y = 2504.246506037 + -2500.75 y = 2504.246506037 + -2500.75 Combine like terms: 2504.246506037 + -2500.75 = 3.496506037 y = 3.496506037 Simplifying y = 3.496506037

Subproblem 2

y + 2500.75 = -2504.246506037 Simplifying y + 2500.75 = -2504.246506037 Reorder the terms: 2500.75 + y = -2504.246506037 Solving 2500.75 + y = -2504.246506037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2500.75' to each side of the equation. 2500.75 + -2500.75 + y = -2504.246506037 + -2500.75 Combine like terms: 2500.75 + -2500.75 = 0.00 0.00 + y = -2504.246506037 + -2500.75 y = -2504.246506037 + -2500.75 Combine like terms: -2504.246506037 + -2500.75 = -5004.996506037 y = -5004.996506037 Simplifying y = -5004.996506037

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.496506037, -5004.996506037}

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