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Simplifying 5x2 + -20x2y + 5z + -20yz = 0 Reorder the terms: 5x2 + -20x2y + -20yz + 5z = 0 Solving 5x2 + -20x2y + -20yz + 5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20yz' to each side of the equation. 5x2 + -20x2y + -20yz + 20yz + 5z = 0 + 20yz Combine like terms: -20yz + 20yz = 0 5x2 + -20x2y + 0 + 5z = 0 + 20yz 5x2 + -20x2y + 5z = 0 + 20yz Remove the zero: 5x2 + -20x2y + 5z = 20yz Add '-5z' to each side of the equation. 5x2 + -20x2y + 5z + -5z = 20yz + -5z Combine like terms: 5z + -5z = 0 5x2 + -20x2y + 0 = 20yz + -5z 5x2 + -20x2y = 20yz + -5z Reorder the terms: 5x2 + -20x2y + -20yz + 5z = 20yz + -20yz + -5z + 5z Combine like terms: 20yz + -20yz = 0 5x2 + -20x2y + -20yz + 5z = 0 + -5z + 5z 5x2 + -20x2y + -20yz + 5z = -5z + 5z Combine like terms: -5z + 5z = 0 5x2 + -20x2y + -20yz + 5z = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(x2 + -4x2y + -4yz + z) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(x2 + -4x2y + -4yz + z)' equal to zero and attempt to solve: Simplifying x2 + -4x2y + -4yz + z = 0 Solving x2 + -4x2y + -4yz + z = 0 Move all terms containing x to the left, all other terms to the right. Add '4yz' to each side of the equation. x2 + -4x2y + -4yz + 4yz + z = 0 + 4yz Combine like terms: -4yz + 4yz = 0 x2 + -4x2y + 0 + z = 0 + 4yz x2 + -4x2y + z = 0 + 4yz Remove the zero: x2 + -4x2y + z = 4yz Add '-1z' to each side of the equation. x2 + -4x2y + z + -1z = 4yz + -1z Combine like terms: z + -1z = 0 x2 + -4x2y + 0 = 4yz + -1z x2 + -4x2y = 4yz + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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