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Simplifying 3x2y + 18xy + -69y = 0 Reorder the terms: 18xy + 3x2y + -69y = 0 Solving 18xy + 3x2y + -69y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(6x + x2 + -23) = 0 Ignore the factor 3.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 + -23)' equal to zero and attempt to solve: Simplifying 6x + x2 + -23 = 0 Reorder the terms: -23 + 6x + x2 = 0 Solving -23 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 6x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 6x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6x + x2 = 0 + 23 6x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 6x + x2 = 23 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 = 23 + 9 Reorder the terms: 9 + 6x + x2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6x + x2 = 32 Factor a perfect square on the left side: (x + 3)(x + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 3 = 5.656854249 Simplifying x + 3 = 5.656854249 Reorder the terms: 3 + x = 5.656854249 Solving 3 + x = 5.656854249 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 = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.656854249 + -3 x = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 x = 2.656854249 Simplifying x = 2.656854249Subproblem 2
x + 3 = -5.656854249 Simplifying x + 3 = -5.656854249 Reorder the terms: 3 + x = -5.656854249 Solving 3 + x = -5.656854249 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 = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.656854249 + -3 x = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 x = -8.656854249 Simplifying x = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.656854249, -8.656854249}Solution
x = {2.656854249, -8.656854249}
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