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Simplifying 6x2y + 66xy + -78y = 0 Reorder the terms: 66xy + 6x2y + -78y = 0 Solving 66xy + 6x2y + -78y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6y'. 6y(11x + x2 + -13) = 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 '(11x + x2 + -13)' equal to zero and attempt to solve: Simplifying 11x + x2 + -13 = 0 Reorder the terms: -13 + 11x + x2 = 0 Solving -13 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 11x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 11x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 11x + x2 = 0 + 13 11x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 11x + x2 = 13 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 13 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 13 + 30.25 Combine like terms: 13 + 30.25 = 43.25 30.25 + 11x + x2 = 43.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 5.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + 5.5 = 6.576473219 Simplifying x + 5.5 = 6.576473219 Reorder the terms: 5.5 + x = 6.576473219 Solving 5.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.576473219 + -5.5 x = 6.576473219 + -5.5 Combine like terms: 6.576473219 + -5.5 = 1.076473219 x = 1.076473219 Simplifying x = 1.076473219Subproblem 2
x + 5.5 = -6.576473219 Simplifying x + 5.5 = -6.576473219 Reorder the terms: 5.5 + x = -6.576473219 Solving 5.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.576473219 + -5.5 x = -6.576473219 + -5.5 Combine like terms: -6.576473219 + -5.5 = -12.076473219 x = -12.076473219 Simplifying x = -12.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.076473219, -12.076473219}Solution
x = {1.076473219, -12.076473219}
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