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Simplifying 3y2 + -8y = 12 Reorder the terms: -8y + 3y2 = 12 Solving -8y + 3y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + -8y + 3y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -8y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -2.666666667y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.666666667y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -2.666666667y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.666666667y + y2 = 0 + 4 -2.666666667y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.666666667y + y2 = 4 The y term is -2.666666667y. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667y + 1.777777780 + y2 = 4 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667y + y2 = 4 + 1.777777780 Combine like terms: 4 + 1.777777780 = 5.77777778 1.777777780 + -2.666666667y + y2 = 5.77777778 Factor a perfect square on the left side: (y + -1.333333334)(y + -1.333333334) = 5.77777778 Calculate the square root of the right side: 2.403700851 Break this problem into two subproblems by setting (y + -1.333333334) equal to 2.403700851 and -2.403700851.Subproblem 1
y + -1.333333334 = 2.403700851 Simplifying y + -1.333333334 = 2.403700851 Reorder the terms: -1.333333334 + y = 2.403700851 Solving -1.333333334 + y = 2.403700851 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + y = 2.403700851 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + y = 2.403700851 + 1.333333334 y = 2.403700851 + 1.333333334 Combine like terms: 2.403700851 + 1.333333334 = 3.737034185 y = 3.737034185 Simplifying y = 3.737034185Subproblem 2
y + -1.333333334 = -2.403700851 Simplifying y + -1.333333334 = -2.403700851 Reorder the terms: -1.333333334 + y = -2.403700851 Solving -1.333333334 + y = -2.403700851 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + y = -2.403700851 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + y = -2.403700851 + 1.333333334 y = -2.403700851 + 1.333333334 Combine like terms: -2.403700851 + 1.333333334 = -1.070367517 y = -1.070367517 Simplifying y = -1.070367517Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.737034185, -1.070367517}
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