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Simplifying 2x2y + 12xy + -38y = 0 Reorder the terms: 12xy + 2x2y + -38y = 0 Solving 12xy + 2x2y + -38y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(6x + x2 + -19) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6x + x2 + -19)' equal to zero and attempt to solve: Simplifying 6x + x2 + -19 = 0 Reorder the terms: -19 + 6x + x2 = 0 Solving -19 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6x + x2 = 0 + 19 6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 6x + x2 = 19 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 19 + 9 Reorder the terms: 9 + 6x + x2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + 6x + x2 = 28 Factor a perfect square on the left side: (x + 3)(x + 3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 3) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 3 = 5.291502622 Simplifying x + 3 = 5.291502622 Reorder the terms: 3 + x = 5.291502622 Solving 3 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.291502622 + -3 x = 5.291502622 + -3 Combine like terms: 5.291502622 + -3 = 2.291502622 x = 2.291502622 Simplifying x = 2.291502622Subproblem 2
x + 3 = -5.291502622 Simplifying x + 3 = -5.291502622 Reorder the terms: 3 + x = -5.291502622 Solving 3 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.291502622 + -3 x = -5.291502622 + -3 Combine like terms: -5.291502622 + -3 = -8.291502622 x = -8.291502622 Simplifying x = -8.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.291502622, -8.291502622}Solution
x = {2.291502622, -8.291502622}
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