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Simplifying 2y2 + -3y + -12 = 0 Reorder the terms: -12 + -3y + 2y2 = 0 Solving -12 + -3y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -1.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -1.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.5y + y2 = 0 + 6 -1.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.5y + y2 = 6 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 6 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 6 + 0.5625 Combine like terms: 6 + 0.5625 = 6.5625 0.5625 + -1.5y + y2 = 6.5625 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (y + -0.75) equal to 2.561737691 and -2.561737691.Subproblem 1
y + -0.75 = 2.561737691 Simplifying y + -0.75 = 2.561737691 Reorder the terms: -0.75 + y = 2.561737691 Solving -0.75 + y = 2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 2.561737691 + 0.75 y = 2.561737691 + 0.75 Combine like terms: 2.561737691 + 0.75 = 3.311737691 y = 3.311737691 Simplifying y = 3.311737691Subproblem 2
y + -0.75 = -2.561737691 Simplifying y + -0.75 = -2.561737691 Reorder the terms: -0.75 + y = -2.561737691 Solving -0.75 + y = -2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -2.561737691 + 0.75 y = -2.561737691 + 0.75 Combine like terms: -2.561737691 + 0.75 = -1.811737691 y = -1.811737691 Simplifying y = -1.811737691Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.311737691, -1.811737691}
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