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Simplifying 3x2y + 21xy + -51y = 0 Reorder the terms: 21xy + 3x2y + -51y = 0 Solving 21xy + 3x2y + -51y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(7x + x2 + -17) = 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 + -17)' equal to zero and attempt to solve: Simplifying 7x + x2 + -17 = 0 Reorder the terms: -17 + 7x + x2 = 0 Solving -17 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 7x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 7x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 7x + x2 = 0 + 17 7x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 7x + x2 = 17 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 = 17 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 17 + 12.25 Combine like terms: 17 + 12.25 = 29.25 12.25 + 7x + x2 = 29.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + 3.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + 3.5 = 5.408326913 Simplifying x + 3.5 = 5.408326913 Reorder the terms: 3.5 + x = 5.408326913 Solving 3.5 + x = 5.408326913 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 = 5.408326913 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.408326913 + -3.5 x = 5.408326913 + -3.5 Combine like terms: 5.408326913 + -3.5 = 1.908326913 x = 1.908326913 Simplifying x = 1.908326913Subproblem 2
x + 3.5 = -5.408326913 Simplifying x + 3.5 = -5.408326913 Reorder the terms: 3.5 + x = -5.408326913 Solving 3.5 + x = -5.408326913 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 = -5.408326913 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.408326913 + -3.5 x = -5.408326913 + -3.5 Combine like terms: -5.408326913 + -3.5 = -8.908326913 x = -8.908326913 Simplifying x = -8.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.908326913, -8.908326913}Solution
x = {1.908326913, -8.908326913}
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