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Simplifying 12y(y + -2) = 24 Reorder the terms: 12y(-2 + y) = 24 (-2 * 12y + y * 12y) = 24 (-24y + 12y2) = 24 Solving -24y + 12y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + -24y + 12y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -24y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + -2y + y2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-2 + -2y + y2)' equal to zero and attempt to solve: Simplifying -2 + -2y + y2 = 0 Solving -2 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -2y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2y + y2 = 0 + 2 -2y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2y + y2 = 2 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 2 + 1 Reorder the terms: 1 + -2y + y2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2y + y2 = 3 Factor a perfect square on the left side: (y + -1)(y + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -1 = 1.732050808 Simplifying y + -1 = 1.732050808 Reorder the terms: -1 + y = 1.732050808 Solving -1 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.732050808 + 1 y = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 y = 2.732050808 Simplifying y = 2.732050808Subproblem 2
y + -1 = -1.732050808 Simplifying y + -1 = -1.732050808 Reorder the terms: -1 + y = -1.732050808 Solving -1 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.732050808 + 1 y = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 y = -0.732050808 Simplifying y = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.732050808, -0.732050808}Solution
y = {2.732050808, -0.732050808}
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