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Simplifying 4x2y + 12xy + -68y = 0 Reorder the terms: 12xy + 4x2y + -68y = 0 Solving 12xy + 4x2y + -68y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4y'. 4y(3x + x2 + -17) = 0 Ignore the factor 4.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 '(3x + x2 + -17)' equal to zero and attempt to solve: Simplifying 3x + x2 + -17 = 0 Reorder the terms: -17 + 3x + x2 = 0 Solving -17 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 3x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 3x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 3x + x2 = 0 + 17 3x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 3x + x2 = 17 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 17 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 17 + 2.25 Combine like terms: 17 + 2.25 = 19.25 2.25 + 3x + x2 = 19.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 1.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 1.5 = 4.387482194 Simplifying x + 1.5 = 4.387482194 Reorder the terms: 1.5 + x = 4.387482194 Solving 1.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.387482194 + -1.5 x = 4.387482194 + -1.5 Combine like terms: 4.387482194 + -1.5 = 2.887482194 x = 2.887482194 Simplifying x = 2.887482194Subproblem 2
x + 1.5 = -4.387482194 Simplifying x + 1.5 = -4.387482194 Reorder the terms: 1.5 + x = -4.387482194 Solving 1.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.387482194 + -1.5 x = -4.387482194 + -1.5 Combine like terms: -4.387482194 + -1.5 = -5.887482194 x = -5.887482194 Simplifying x = -5.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.887482194, -5.887482194}Solution
x = {2.887482194, -5.887482194}
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