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Simplifying y2 + -2y + -19 = 0 Reorder the terms: -19 + -2y + y2 = 0 Solving -19 + -2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -2y + 19 + y2 = 0 + 19 Reorder the terms: -19 + 19 + -2y + y2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2y + y2 = 0 + 19 -2y + y2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2y + y2 = 19 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 19 + 1 Reorder the terms: 1 + -2y + y2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + -2y + y2 = 20 Factor a perfect square on the left side: (y + -1)(y + -1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y + -1) equal to 4.472135955 and -4.472135955.Subproblem 1
y + -1 = 4.472135955 Simplifying y + -1 = 4.472135955 Reorder the terms: -1 + y = 4.472135955 Solving -1 + y = 4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.472135955 + 1 y = 4.472135955 + 1 Combine like terms: 4.472135955 + 1 = 5.472135955 y = 5.472135955 Simplifying y = 5.472135955Subproblem 2
y + -1 = -4.472135955 Simplifying y + -1 = -4.472135955 Reorder the terms: -1 + y = -4.472135955 Solving -1 + y = -4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.472135955 + 1 y = -4.472135955 + 1 Combine like terms: -4.472135955 + 1 = -3.472135955 y = -3.472135955 Simplifying y = -3.472135955Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.472135955, -3.472135955}
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