14y^2-7000y-3=0

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Solution for 14y^2-7000y-3=0 equation:


Simplifying
14y2 + -7000y + -3 = 0

Reorder the terms:
-3 + -7000y + 14y2 = 0

Solving
-3 + -7000y + 14y2 = 0

Solving for variable 'y'.

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

Divide each side by '14'.
-0.2142857143 + -500y + y2 = 0

Move the constant term to the right:

Add '0.2142857143' to each side of the equation.
-0.2142857143 + -500y + 0.2142857143 + y2 = 0 + 0.2142857143

Reorder the terms:
-0.2142857143 + 0.2142857143 + -500y + y2 = 0 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + -500y + y2 = 0 + 0.2142857143
-500y + y2 = 0 + 0.2142857143

Combine like terms: 0 + 0.2142857143 = 0.2142857143
-500y + y2 = 0.2142857143

The y term is -500y.  Take half its coefficient (-250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
-500y + 62500 + y2 = 0.2142857143 + 62500

Reorder the terms:
62500 + -500y + y2 = 0.2142857143 + 62500

Combine like terms: 0.2142857143 + 62500 = 62500.2142857143
62500 + -500y + y2 = 62500.2142857143

Factor a perfect square on the left side:
(y + -250)(y + -250) = 62500.2142857143

Calculate the square root of the right side: 250.000428571

Break this problem into two subproblems by setting 
(y + -250) equal to 250.000428571 and -250.000428571.

Subproblem 1

y + -250 = 250.000428571 Simplifying y + -250 = 250.000428571 Reorder the terms: -250 + y = 250.000428571 Solving -250 + y = 250.000428571 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + y = 250.000428571 + 250 Combine like terms: -250 + 250 = 0 0 + y = 250.000428571 + 250 y = 250.000428571 + 250 Combine like terms: 250.000428571 + 250 = 500.000428571 y = 500.000428571 Simplifying y = 500.000428571

Subproblem 2

y + -250 = -250.000428571 Simplifying y + -250 = -250.000428571 Reorder the terms: -250 + y = -250.000428571 Solving -250 + y = -250.000428571 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + y = -250.000428571 + 250 Combine like terms: -250 + 250 = 0 0 + y = -250.000428571 + 250 y = -250.000428571 + 250 Combine like terms: -250.000428571 + 250 = -0.000428571 y = -0.000428571 Simplifying y = -0.000428571

Solution

The solution to the problem is based on the solutions from the subproblems. y = {500.000428571, -0.000428571}

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