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Simplifying -3y2 + 12y = 3.4225 Reorder the terms: 12y + -3y2 = 3.4225 Solving 12y + -3y2 = 3.4225 Solving for variable 'y'. Reorder the terms: -3.4225 + 12y + -3y2 = 3.4225 + -3.4225 Combine like terms: 3.4225 + -3.4225 = 0.0000 -3.4225 + 12y + -3y2 = 0.0000 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.140833333 + -4y + y2 = 0.0000 Move the constant term to the right: Add '-1.140833333' to each side of the equation. 1.140833333 + -4y + -1.140833333 + y2 = 0.0000 + -1.140833333 Reorder the terms: 1.140833333 + -1.140833333 + -4y + y2 = 0.0000 + -1.140833333 Combine like terms: 1.140833333 + -1.140833333 = 0.000000000 0.000000000 + -4y + y2 = 0.0000 + -1.140833333 -4y + y2 = 0.0000 + -1.140833333 Combine like terms: 0.0000 + -1.140833333 = -1.140833333 -4y + y2 = -1.140833333 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 = -1.140833333 + 4 Reorder the terms: 4 + -4y + y2 = -1.140833333 + 4 Combine like terms: -1.140833333 + 4 = 2.859166667 4 + -4y + y2 = 2.859166667 Factor a perfect square on the left side: (y + -2)(y + -2) = 2.859166667 Calculate the square root of the right side: 1.690907055 Break this problem into two subproblems by setting (y + -2) equal to 1.690907055 and -1.690907055.Subproblem 1
y + -2 = 1.690907055 Simplifying y + -2 = 1.690907055 Reorder the terms: -2 + y = 1.690907055 Solving -2 + y = 1.690907055 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 = 1.690907055 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.690907055 + 2 y = 1.690907055 + 2 Combine like terms: 1.690907055 + 2 = 3.690907055 y = 3.690907055 Simplifying y = 3.690907055Subproblem 2
y + -2 = -1.690907055 Simplifying y + -2 = -1.690907055 Reorder the terms: -2 + y = -1.690907055 Solving -2 + y = -1.690907055 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 = -1.690907055 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.690907055 + 2 y = -1.690907055 + 2 Combine like terms: -1.690907055 + 2 = 0.309092945 y = 0.309092945 Simplifying y = 0.309092945Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.690907055, 0.309092945}
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