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Simplifying 2x3y + -18x2y + -4xy = 0 Reorder the terms: -4xy + -18x2y + 2x3y = 0 Solving -4xy + -18x2y + 2x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2xy'. 2xy(-2 + -9x + x2) = 0 Ignore the factor 2.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 + -9x + x2)' equal to zero and attempt to solve: Simplifying -2 + -9x + x2 = 0 Solving -2 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -9x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -9x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -9x + x2 = 0 + 2 -9x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -9x + x2 = 2 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 2 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 2 + 20.25 Combine like terms: 2 + 20.25 = 22.25 20.25 + -9x + x2 = 22.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -4.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -4.5 = 4.716990566 Simplifying x + -4.5 = 4.716990566 Reorder the terms: -4.5 + x = 4.716990566 Solving -4.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.716990566 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.716990566 + 4.5 x = 4.716990566 + 4.5 Combine like terms: 4.716990566 + 4.5 = 9.216990566 x = 9.216990566 Simplifying x = 9.216990566Subproblem 2
x + -4.5 = -4.716990566 Simplifying x + -4.5 = -4.716990566 Reorder the terms: -4.5 + x = -4.716990566 Solving -4.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.716990566 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.716990566 + 4.5 x = -4.716990566 + 4.5 Combine like terms: -4.716990566 + 4.5 = -0.216990566 x = -0.216990566 Simplifying x = -0.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.216990566, -0.216990566}Solution
x = {9.216990566, -0.216990566}
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