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Simplifying 7y2 + 65y + -12 = 0 Reorder the terms: -12 + 65y + 7y2 = 0 Solving -12 + 65y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + 9.285714286y + y2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + 9.285714286y + 1.714285714 + y2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + 9.285714286y + y2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + 9.285714286y + y2 = 0 + 1.714285714 9.285714286y + y2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 9.285714286y + y2 = 1.714285714 The y term is 9.285714286y. Take half its coefficient (4.642857143). Square it (21.55612245) and add it to both sides. Add '21.55612245' to each side of the equation. 9.285714286y + 21.55612245 + y2 = 1.714285714 + 21.55612245 Reorder the terms: 21.55612245 + 9.285714286y + y2 = 1.714285714 + 21.55612245 Combine like terms: 1.714285714 + 21.55612245 = 23.270408164 21.55612245 + 9.285714286y + y2 = 23.270408164 Factor a perfect square on the left side: (y + 4.642857143)(y + 4.642857143) = 23.270408164 Calculate the square root of the right side: 4.823941144 Break this problem into two subproblems by setting (y + 4.642857143) equal to 4.823941144 and -4.823941144.Subproblem 1
y + 4.642857143 = 4.823941144 Simplifying y + 4.642857143 = 4.823941144 Reorder the terms: 4.642857143 + y = 4.823941144 Solving 4.642857143 + y = 4.823941144 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.642857143' to each side of the equation. 4.642857143 + -4.642857143 + y = 4.823941144 + -4.642857143 Combine like terms: 4.642857143 + -4.642857143 = 0.000000000 0.000000000 + y = 4.823941144 + -4.642857143 y = 4.823941144 + -4.642857143 Combine like terms: 4.823941144 + -4.642857143 = 0.181084001 y = 0.181084001 Simplifying y = 0.181084001Subproblem 2
y + 4.642857143 = -4.823941144 Simplifying y + 4.642857143 = -4.823941144 Reorder the terms: 4.642857143 + y = -4.823941144 Solving 4.642857143 + y = -4.823941144 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.642857143' to each side of the equation. 4.642857143 + -4.642857143 + y = -4.823941144 + -4.642857143 Combine like terms: 4.642857143 + -4.642857143 = 0.000000000 0.000000000 + y = -4.823941144 + -4.642857143 y = -4.823941144 + -4.642857143 Combine like terms: -4.823941144 + -4.642857143 = -9.466798287 y = -9.466798287 Simplifying y = -9.466798287Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.181084001, -9.466798287}
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