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Simplifying 8x2y + 39xy + -84y = 0 Reorder the terms: 39xy + 8x2y + -84y = 0 Solving 39xy + 8x2y + -84y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'y'. y(39x + 8x2 + -84) = 0Subproblem 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 '(39x + 8x2 + -84)' equal to zero and attempt to solve: Simplifying 39x + 8x2 + -84 = 0 Reorder the terms: -84 + 39x + 8x2 = 0 Solving -84 + 39x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10.5 + 4.875x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 4.875x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 4.875x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 4.875x + x2 = 0 + 10.5 4.875x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 4.875x + x2 = 10.5 The x term is 4.875x. Take half its coefficient (2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. 4.875x + 5.94140625 + x2 = 10.5 + 5.94140625 Reorder the terms: 5.94140625 + 4.875x + x2 = 10.5 + 5.94140625 Combine like terms: 10.5 + 5.94140625 = 16.44140625 5.94140625 + 4.875x + x2 = 16.44140625 Factor a perfect square on the left side: (x + 2.4375)(x + 2.4375) = 16.44140625 Calculate the square root of the right side: 4.054800396 Break this problem into two subproblems by setting (x + 2.4375) equal to 4.054800396 and -4.054800396.Subproblem 1
x + 2.4375 = 4.054800396 Simplifying x + 2.4375 = 4.054800396 Reorder the terms: 2.4375 + x = 4.054800396 Solving 2.4375 + x = 4.054800396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4375' to each side of the equation. 2.4375 + -2.4375 + x = 4.054800396 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + x = 4.054800396 + -2.4375 x = 4.054800396 + -2.4375 Combine like terms: 4.054800396 + -2.4375 = 1.617300396 x = 1.617300396 Simplifying x = 1.617300396Subproblem 2
x + 2.4375 = -4.054800396 Simplifying x + 2.4375 = -4.054800396 Reorder the terms: 2.4375 + x = -4.054800396 Solving 2.4375 + x = -4.054800396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4375' to each side of the equation. 2.4375 + -2.4375 + x = -4.054800396 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + x = -4.054800396 + -2.4375 x = -4.054800396 + -2.4375 Combine like terms: -4.054800396 + -2.4375 = -6.492300396 x = -6.492300396 Simplifying x = -6.492300396Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.617300396, -6.492300396}Solution
x = {1.617300396, -6.492300396}
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