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Simplifying 3x2y + 21xy + -87y = 0 Reorder the terms: 21xy + 3x2y + -87y = 0 Solving 21xy + 3x2y + -87y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(7x + x2 + -29) = 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 '(7x + x2 + -29)' equal to zero and attempt to solve: Simplifying 7x + x2 + -29 = 0 Reorder the terms: -29 + 7x + x2 = 0 Solving -29 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 7x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 7x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 7x + x2 = 0 + 29 7x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 7x + x2 = 29 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 29 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 29 + 12.25 Combine like terms: 29 + 12.25 = 41.25 12.25 + 7x + x2 = 41.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 3.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 3.5 = 6.422616289 Simplifying x + 3.5 = 6.422616289 Reorder the terms: 3.5 + x = 6.422616289 Solving 3.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.422616289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.422616289 + -3.5 x = 6.422616289 + -3.5 Combine like terms: 6.422616289 + -3.5 = 2.922616289 x = 2.922616289 Simplifying x = 2.922616289Subproblem 2
x + 3.5 = -6.422616289 Simplifying x + 3.5 = -6.422616289 Reorder the terms: 3.5 + x = -6.422616289 Solving 3.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.422616289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.422616289 + -3.5 x = -6.422616289 + -3.5 Combine like terms: -6.422616289 + -3.5 = -9.922616289 x = -9.922616289 Simplifying x = -9.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.922616289, -9.922616289}Solution
x = {2.922616289, -9.922616289}
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