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Simplifying 2y2 + -4y + -14 + -1y2 = 0 Reorder the terms: -14 + -4y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 -14 + -4y + 1y2 = 0 Solving -14 + -4y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -4y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + -4y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -4y + y2 = 0 + 14 -4y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 -4y + y2 = 14 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 = 14 + 4 Reorder the terms: 4 + -4y + y2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + -4y + y2 = 18 Factor a perfect square on the left side: (y + -2)(y + -2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + -2) equal to 4.242640687 and -4.242640687.Subproblem 1
y + -2 = 4.242640687 Simplifying y + -2 = 4.242640687 Reorder the terms: -2 + y = 4.242640687 Solving -2 + y = 4.242640687 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 = 4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + y = 4.242640687 + 2 y = 4.242640687 + 2 Combine like terms: 4.242640687 + 2 = 6.242640687 y = 6.242640687 Simplifying y = 6.242640687Subproblem 2
y + -2 = -4.242640687 Simplifying y + -2 = -4.242640687 Reorder the terms: -2 + y = -4.242640687 Solving -2 + y = -4.242640687 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 = -4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + y = -4.242640687 + 2 y = -4.242640687 + 2 Combine like terms: -4.242640687 + 2 = -2.242640687 y = -2.242640687 Simplifying y = -2.242640687Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.242640687, -2.242640687}
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