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Simplifying 2x2y + 30xy + -38y = 0 Reorder the terms: 30xy + 2x2y + -38y = 0 Solving 30xy + 2x2y + -38y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(15x + 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 '(15x + x2 + -19)' equal to zero and attempt to solve: Simplifying 15x + x2 + -19 = 0 Reorder the terms: -19 + 15x + x2 = 0 Solving -19 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 15x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 15x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 15x + x2 = 0 + 19 15x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 15x + x2 = 19 The x term is 15x. 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. 15x + 56.25 + x2 = 19 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 19 + 56.25 Combine like terms: 19 + 56.25 = 75.25 56.25 + 15x + x2 = 75.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + 7.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + 7.5 = 8.674675786 Simplifying x + 7.5 = 8.674675786 Reorder the terms: 7.5 + x = 8.674675786 Solving 7.5 + x = 8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.674675786 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.674675786 + -7.5 x = 8.674675786 + -7.5 Combine like terms: 8.674675786 + -7.5 = 1.174675786 x = 1.174675786 Simplifying x = 1.174675786Subproblem 2
x + 7.5 = -8.674675786 Simplifying x + 7.5 = -8.674675786 Reorder the terms: 7.5 + x = -8.674675786 Solving 7.5 + x = -8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.674675786 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.674675786 + -7.5 x = -8.674675786 + -7.5 Combine like terms: -8.674675786 + -7.5 = -16.174675786 x = -16.174675786 Simplifying x = -16.174675786Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.174675786, -16.174675786}Solution
x = {1.174675786, -16.174675786}
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