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Simplifying 7y2 + -43 = -35y Reorder the terms: -43 + 7y2 = -35y Solving -43 + 7y2 = -35y Solving for variable 'y'. Reorder the terms: -43 + 35y + 7y2 = -35y + 35y Combine like terms: -35y + 35y = 0 -43 + 35y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.142857143 + 5y + y2 = 0 Move the constant term to the right: Add '6.142857143' to each side of the equation. -6.142857143 + 5y + 6.142857143 + y2 = 0 + 6.142857143 Reorder the terms: -6.142857143 + 6.142857143 + 5y + y2 = 0 + 6.142857143 Combine like terms: -6.142857143 + 6.142857143 = 0.000000000 0.000000000 + 5y + y2 = 0 + 6.142857143 5y + y2 = 0 + 6.142857143 Combine like terms: 0 + 6.142857143 = 6.142857143 5y + y2 = 6.142857143 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = 6.142857143 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 6.142857143 + 6.25 Combine like terms: 6.142857143 + 6.25 = 12.392857143 6.25 + 5y + y2 = 12.392857143 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 12.392857143 Calculate the square root of the right side: 3.520349009 Break this problem into two subproblems by setting (y + 2.5) equal to 3.520349009 and -3.520349009.Subproblem 1
y + 2.5 = 3.520349009 Simplifying y + 2.5 = 3.520349009 Reorder the terms: 2.5 + y = 3.520349009 Solving 2.5 + y = 3.520349009 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 3.520349009 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 3.520349009 + -2.5 y = 3.520349009 + -2.5 Combine like terms: 3.520349009 + -2.5 = 1.020349009 y = 1.020349009 Simplifying y = 1.020349009Subproblem 2
y + 2.5 = -3.520349009 Simplifying y + 2.5 = -3.520349009 Reorder the terms: 2.5 + y = -3.520349009 Solving 2.5 + y = -3.520349009 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -3.520349009 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -3.520349009 + -2.5 y = -3.520349009 + -2.5 Combine like terms: -3.520349009 + -2.5 = -6.020349009 y = -6.020349009 Simplifying y = -6.020349009Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.020349009, -6.020349009}
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