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Simplifying y2 + 6y + -19 = 0 Reorder the terms: -19 + 6y + y2 = 0 Solving -19 + 6y + 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 + 6y + 19 + y2 = 0 + 19 Reorder the terms: -19 + 19 + 6y + y2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6y + y2 = 0 + 19 6y + y2 = 0 + 19 Combine like terms: 0 + 19 = 19 6y + y2 = 19 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 19 + 9 Reorder the terms: 9 + 6y + y2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + 6y + y2 = 28 Factor a perfect square on the left side: (y + 3)(y + 3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + 3) equal to 5.291502622 and -5.291502622.Subproblem 1
y + 3 = 5.291502622 Simplifying y + 3 = 5.291502622 Reorder the terms: 3 + y = 5.291502622 Solving 3 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + y = 5.291502622 + -3 y = 5.291502622 + -3 Combine like terms: 5.291502622 + -3 = 2.291502622 y = 2.291502622 Simplifying y = 2.291502622Subproblem 2
y + 3 = -5.291502622 Simplifying y + 3 = -5.291502622 Reorder the terms: 3 + y = -5.291502622 Solving 3 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + y = -5.291502622 + -3 y = -5.291502622 + -3 Combine like terms: -5.291502622 + -3 = -8.291502622 y = -8.291502622 Simplifying y = -8.291502622Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.291502622, -8.291502622}
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