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Simplifying 3y2 + -8y + 4 + -3y + 8 + -2y2 = 0 Reorder the terms: 4 + 8 + -8y + -3y + 3y2 + -2y2 = 0 Combine like terms: 4 + 8 = 12 12 + -8y + -3y + 3y2 + -2y2 = 0 Combine like terms: -8y + -3y = -11y 12 + -11y + 3y2 + -2y2 = 0 Combine like terms: 3y2 + -2y2 = 1y2 12 + -11y + 1y2 = 0 Solving 12 + -11y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -11y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -11y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -11y + y2 = 0 + -12 -11y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -11y + y2 = -12 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -12 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + -11y + y2 = 18.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + -5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + -5.5 = 4.272001873 Simplifying y + -5.5 = 4.272001873 Reorder the terms: -5.5 + y = 4.272001873 Solving -5.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 4.272001873 + 5.5 y = 4.272001873 + 5.5 Combine like terms: 4.272001873 + 5.5 = 9.772001873 y = 9.772001873 Simplifying y = 9.772001873Subproblem 2
y + -5.5 = -4.272001873 Simplifying y + -5.5 = -4.272001873 Reorder the terms: -5.5 + y = -4.272001873 Solving -5.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -4.272001873 + 5.5 y = -4.272001873 + 5.5 Combine like terms: -4.272001873 + 5.5 = 1.227998127 y = 1.227998127 Simplifying y = 1.227998127Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.772001873, 1.227998127}
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