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Simplifying 4y * y + -1 = 1528y Multiply y * y 4y2 + -1 = 1528y Reorder the terms: -1 + 4y2 = 1528y Solving -1 + 4y2 = 1528y Solving for variable 'y'. Reorder the terms: -1 + -1528y + 4y2 = 1528y + -1528y Combine like terms: 1528y + -1528y = 0 -1 + -1528y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -382y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -382y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -382y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -382y + y2 = 0 + 0.25 -382y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -382y + y2 = 0.25 The y term is -382y. Take half its coefficient (-191). Square it (36481) and add it to both sides. Add '36481' to each side of the equation. -382y + 36481 + y2 = 0.25 + 36481 Reorder the terms: 36481 + -382y + y2 = 0.25 + 36481 Combine like terms: 0.25 + 36481 = 36481.25 36481 + -382y + y2 = 36481.25 Factor a perfect square on the left side: (y + -191)(y + -191) = 36481.25 Calculate the square root of the right side: 191.000654449 Break this problem into two subproblems by setting (y + -191) equal to 191.000654449 and -191.000654449.Subproblem 1
y + -191 = 191.000654449 Simplifying y + -191 = 191.000654449 Reorder the terms: -191 + y = 191.000654449 Solving -191 + y = 191.000654449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '191' to each side of the equation. -191 + 191 + y = 191.000654449 + 191 Combine like terms: -191 + 191 = 0 0 + y = 191.000654449 + 191 y = 191.000654449 + 191 Combine like terms: 191.000654449 + 191 = 382.000654449 y = 382.000654449 Simplifying y = 382.000654449Subproblem 2
y + -191 = -191.000654449 Simplifying y + -191 = -191.000654449 Reorder the terms: -191 + y = -191.000654449 Solving -191 + y = -191.000654449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '191' to each side of the equation. -191 + 191 + y = -191.000654449 + 191 Combine like terms: -191 + 191 = 0 0 + y = -191.000654449 + 191 y = -191.000654449 + 191 Combine like terms: -191.000654449 + 191 = -0.000654449 y = -0.000654449 Simplifying y = -0.000654449Solution
The solution to the problem is based on the solutions from the subproblems. y = {382.000654449, -0.000654449}
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