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Simplifying 7y(18y + -54) = 71 Reorder the terms: 7y(-54 + 18y) = 71 (-54 * 7y + 18y * 7y) = 71 (-378y + 126y2) = 71 Solving -378y + 126y2 = 71 Solving for variable 'y'. Reorder the terms: -71 + -378y + 126y2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + -378y + 126y2 = 0 Begin completing the square. Divide all terms by 126 the coefficient of the squared term: Divide each side by '126'. -0.5634920635 + -3y + y2 = 0 Move the constant term to the right: Add '0.5634920635' to each side of the equation. -0.5634920635 + -3y + 0.5634920635 + y2 = 0 + 0.5634920635 Reorder the terms: -0.5634920635 + 0.5634920635 + -3y + y2 = 0 + 0.5634920635 Combine like terms: -0.5634920635 + 0.5634920635 = 0.0000000000 0.0000000000 + -3y + y2 = 0 + 0.5634920635 -3y + y2 = 0 + 0.5634920635 Combine like terms: 0 + 0.5634920635 = 0.5634920635 -3y + y2 = 0.5634920635 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 0.5634920635 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 0.5634920635 + 2.25 Combine like terms: 0.5634920635 + 2.25 = 2.8134920635 2.25 + -3y + y2 = 2.8134920635 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 2.8134920635 Calculate the square root of the right side: 1.677346733 Break this problem into two subproblems by setting (y + -1.5) equal to 1.677346733 and -1.677346733.Subproblem 1
y + -1.5 = 1.677346733 Simplifying y + -1.5 = 1.677346733 Reorder the terms: -1.5 + y = 1.677346733 Solving -1.5 + y = 1.677346733 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.677346733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.677346733 + 1.5 y = 1.677346733 + 1.5 Combine like terms: 1.677346733 + 1.5 = 3.177346733 y = 3.177346733 Simplifying y = 3.177346733Subproblem 2
y + -1.5 = -1.677346733 Simplifying y + -1.5 = -1.677346733 Reorder the terms: -1.5 + y = -1.677346733 Solving -1.5 + y = -1.677346733 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.677346733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.677346733 + 1.5 y = -1.677346733 + 1.5 Combine like terms: -1.677346733 + 1.5 = -0.177346733 y = -0.177346733 Simplifying y = -0.177346733Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.177346733, -0.177346733}
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