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Simplifying 6y2 + -16y + -9 = 0 Reorder the terms: -9 + -16y + 6y2 = 0 Solving -9 + -16y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -2.666666667y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.666666667y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.666666667y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.666666667y + y2 = 0 + 1.5 -2.666666667y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.666666667y + y2 = 1.5 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 = 1.5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667y + y2 = 1.5 + 1.777777780 Combine like terms: 1.5 + 1.777777780 = 3.27777778 1.777777780 + -2.666666667y + y2 = 3.27777778 Factor a perfect square on the left side: (y + -1.333333334)(y + -1.333333334) = 3.27777778 Calculate the square root of the right side: 1.810463416 Break this problem into two subproblems by setting (y + -1.333333334) equal to 1.810463416 and -1.810463416.Subproblem 1
y + -1.333333334 = 1.810463416 Simplifying y + -1.333333334 = 1.810463416 Reorder the terms: -1.333333334 + y = 1.810463416 Solving -1.333333334 + y = 1.810463416 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 = 1.810463416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + y = 1.810463416 + 1.333333334 y = 1.810463416 + 1.333333334 Combine like terms: 1.810463416 + 1.333333334 = 3.14379675 y = 3.14379675 Simplifying y = 3.14379675Subproblem 2
y + -1.333333334 = -1.810463416 Simplifying y + -1.333333334 = -1.810463416 Reorder the terms: -1.333333334 + y = -1.810463416 Solving -1.333333334 + y = -1.810463416 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 = -1.810463416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + y = -1.810463416 + 1.333333334 y = -1.810463416 + 1.333333334 Combine like terms: -1.810463416 + 1.333333334 = -0.477130082 y = -0.477130082 Simplifying y = -0.477130082Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.14379675, -0.477130082}
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