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Simplifying 6x2y + 24xy + -66y = 0 Reorder the terms: 24xy + 6x2y + -66y = 0 Solving 24xy + 6x2y + -66y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6y'. 6y(4x + x2 + -11) = 0 Ignore the factor 6.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 '(4x + x2 + -11)' equal to zero and attempt to solve: Simplifying 4x + x2 + -11 = 0 Reorder the terms: -11 + 4x + x2 = 0 Solving -11 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4x + x2 = 0 + 11 4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 4x + x2 = 11 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + 4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4x + x2 = 15 Factor a perfect square on the left side: (x + 2)(x + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 2 = 3.872983346 Simplifying x + 2 = 3.872983346 Reorder the terms: 2 + x = 3.872983346 Solving 2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.872983346 + -2 x = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 x = 1.872983346 Simplifying x = 1.872983346Subproblem 2
x + 2 = -3.872983346 Simplifying x + 2 = -3.872983346 Reorder the terms: 2 + x = -3.872983346 Solving 2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.872983346 + -2 x = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 x = -5.872983346 Simplifying x = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.872983346, -5.872983346}Solution
x = {1.872983346, -5.872983346}
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