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Simplifying 14y2 + -7000y = 3 Reorder the terms: -7000y + 14y2 = 3 Solving -7000y + 14y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + -7000y + 14y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -7000y + 14y2 = 0 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 = 500.000428571Subproblem 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 = -0.000428571Solution
The solution to the problem is based on the solutions from the subproblems. y = {500.000428571, -0.000428571}
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