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Simplifying (36y2) + -5 = y + -18y2 Reorder the terms: -5 + (36y2) = y + -18y2 Solving -5 + (36y2) = y + -18y2 Solving for variable 'y'. Reorder the terms: -5 + -1y + (36y2) + 18y2 = y + -18y2 + -1y + 18y2 Combine like terms: (36y2) + 18y2 = 54y2 -5 + -1y + 54y2 = y + -18y2 + -1y + 18y2 Reorder the terms: -5 + -1y + 54y2 = y + -1y + -18y2 + 18y2 Combine like terms: y + -1y = 0 -5 + -1y + 54y2 = 0 + -18y2 + 18y2 -5 + -1y + 54y2 = -18y2 + 18y2 Combine like terms: -18y2 + 18y2 = 0 -5 + -1y + 54y2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.09259259259 + -0.01851851852y + y2 = 0 Move the constant term to the right: Add '0.09259259259' to each side of the equation. -0.09259259259 + -0.01851851852y + 0.09259259259 + y2 = 0 + 0.09259259259 Reorder the terms: -0.09259259259 + 0.09259259259 + -0.01851851852y + y2 = 0 + 0.09259259259 Combine like terms: -0.09259259259 + 0.09259259259 = 0.00000000000 0.00000000000 + -0.01851851852y + y2 = 0 + 0.09259259259 -0.01851851852y + y2 = 0 + 0.09259259259 Combine like terms: 0 + 0.09259259259 = 0.09259259259 -0.01851851852y + y2 = 0.09259259259 The y term is -0.01851851852y. Take half its coefficient (-0.00925925926). Square it (0.00008573388204) and add it to both sides. Add '0.00008573388204' to each side of the equation. -0.01851851852y + 0.00008573388204 + y2 = 0.09259259259 + 0.00008573388204 Reorder the terms: 0.00008573388204 + -0.01851851852y + y2 = 0.09259259259 + 0.00008573388204 Combine like terms: 0.09259259259 + 0.00008573388204 = 0.09267832647204 0.00008573388204 + -0.01851851852y + y2 = 0.09267832647204 Factor a perfect square on the left side: (y + -0.00925925926)(y + -0.00925925926) = 0.09267832647204 Calculate the square root of the right side: 0.304431152 Break this problem into two subproblems by setting (y + -0.00925925926) equal to 0.304431152 and -0.304431152.Subproblem 1
y + -0.00925925926 = 0.304431152 Simplifying y + -0.00925925926 = 0.304431152 Reorder the terms: -0.00925925926 + y = 0.304431152 Solving -0.00925925926 + y = 0.304431152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.00925925926' to each side of the equation. -0.00925925926 + 0.00925925926 + y = 0.304431152 + 0.00925925926 Combine like terms: -0.00925925926 + 0.00925925926 = 0.00000000000 0.00000000000 + y = 0.304431152 + 0.00925925926 y = 0.304431152 + 0.00925925926 Combine like terms: 0.304431152 + 0.00925925926 = 0.31369041126 y = 0.31369041126 Simplifying y = 0.31369041126Subproblem 2
y + -0.00925925926 = -0.304431152 Simplifying y + -0.00925925926 = -0.304431152 Reorder the terms: -0.00925925926 + y = -0.304431152 Solving -0.00925925926 + y = -0.304431152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.00925925926' to each side of the equation. -0.00925925926 + 0.00925925926 + y = -0.304431152 + 0.00925925926 Combine like terms: -0.00925925926 + 0.00925925926 = 0.00000000000 0.00000000000 + y = -0.304431152 + 0.00925925926 y = -0.304431152 + 0.00925925926 Combine like terms: -0.304431152 + 0.00925925926 = -0.29517189274 y = -0.29517189274 Simplifying y = -0.29517189274Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.31369041126, -0.29517189274}
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