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Simplifying y2 + -4 = 2y2 + -15y + 34 Reorder the terms: -4 + y2 = 2y2 + -15y + 34 Reorder the terms: -4 + y2 = 34 + -15y + 2y2 Solving -4 + y2 = 34 + -15y + 2y2 Solving for variable 'y'. Reorder the terms: -4 + -34 + 15y + y2 + -2y2 = 34 + -15y + 2y2 + -34 + 15y + -2y2 Combine like terms: -4 + -34 = -38 -38 + 15y + y2 + -2y2 = 34 + -15y + 2y2 + -34 + 15y + -2y2 Combine like terms: y2 + -2y2 = -1y2 -38 + 15y + -1y2 = 34 + -15y + 2y2 + -34 + 15y + -2y2 Reorder the terms: -38 + 15y + -1y2 = 34 + -34 + -15y + 15y + 2y2 + -2y2 Combine like terms: 34 + -34 = 0 -38 + 15y + -1y2 = 0 + -15y + 15y + 2y2 + -2y2 -38 + 15y + -1y2 = -15y + 15y + 2y2 + -2y2 Combine like terms: -15y + 15y = 0 -38 + 15y + -1y2 = 0 + 2y2 + -2y2 -38 + 15y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -38 + 15y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 38 + -15y + y2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -15y + -38 + y2 = 0 + -38 Reorder the terms: 38 + -38 + -15y + y2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -15y + y2 = 0 + -38 -15y + y2 = 0 + -38 Combine like terms: 0 + -38 = -38 -15y + y2 = -38 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -38 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -38 + 56.25 Combine like terms: -38 + 56.25 = 18.25 56.25 + -15y + y2 = 18.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + -7.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + -7.5 = 4.272001873 Simplifying y + -7.5 = 4.272001873 Reorder the terms: -7.5 + y = 4.272001873 Solving -7.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 4.272001873 + 7.5 y = 4.272001873 + 7.5 Combine like terms: 4.272001873 + 7.5 = 11.772001873 y = 11.772001873 Simplifying y = 11.772001873Subproblem 2
y + -7.5 = -4.272001873 Simplifying y + -7.5 = -4.272001873 Reorder the terms: -7.5 + y = -4.272001873 Solving -7.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -4.272001873 + 7.5 y = -4.272001873 + 7.5 Combine like terms: -4.272001873 + 7.5 = 3.227998127 y = 3.227998127 Simplifying y = 3.227998127Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.772001873, 3.227998127}
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