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Simplifying -1y2 + 4y = 1 Reorder the terms: 4y + -1y2 = 1 Solving 4y + -1y2 = 1 Solving for variable 'y'. Reorder the terms: -1 + 4y + -1y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -4y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -4y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4y + y2 = 0 + -1 -4y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4y + y2 = -1 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -1 + 4 Reorder the terms: 4 + -4y + y2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4y + y2 = 3 Factor a perfect square on the left side: (y + -2)(y + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -2 = 1.732050808 Simplifying y + -2 = 1.732050808 Reorder the terms: -2 + y = 1.732050808 Solving -2 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.732050808 + 2 y = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 y = 3.732050808 Simplifying y = 3.732050808Subproblem 2
y + -2 = -1.732050808 Simplifying y + -2 = -1.732050808 Reorder the terms: -2 + y = -1.732050808 Solving -2 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.732050808 + 2 y = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 y = 0.267949192 Simplifying y = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.732050808, 0.267949192}
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