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Simplifying 3x3y + 15x2y + -6xy = 0 Reorder the terms: -6xy + 15x2y + 3x3y = 0 Solving -6xy + 15x2y + 3x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3xy'. 3xy(-2 + 5x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 0 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 '(-2 + 5x + x2)' equal to zero and attempt to solve: Simplifying -2 + 5x + x2 = 0 Solving -2 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x + x2 = 0 + 2 5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 5x + x2 = 2 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + 5x + x2 = 8.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 2.5 = 2.872281323 Simplifying x + 2.5 = 2.872281323 Reorder the terms: 2.5 + x = 2.872281323 Solving 2.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.872281323 + -2.5 x = 2.872281323 + -2.5 Combine like terms: 2.872281323 + -2.5 = 0.372281323 x = 0.372281323 Simplifying x = 0.372281323Subproblem 2
x + 2.5 = -2.872281323 Simplifying x + 2.5 = -2.872281323 Reorder the terms: 2.5 + x = -2.872281323 Solving 2.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.872281323 + -2.5 x = -2.872281323 + -2.5 Combine like terms: -2.872281323 + -2.5 = -5.372281323 x = -5.372281323 Simplifying x = -5.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.372281323, -5.372281323}Solution
x = {0.372281323, -5.372281323}
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