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Simplifying (6x3y2 + 7x2y2 + 7xy2) + (6x3y2 + -3x2y2 + -3xy2) = 0 Reorder the terms: (7xy2 + 7x2y2 + 6x3y2) + (6x3y2 + -3x2y2 + -3xy2) = 0 Remove parenthesis around (7xy2 + 7x2y2 + 6x3y2) 7xy2 + 7x2y2 + 6x3y2 + (6x3y2 + -3x2y2 + -3xy2) = 0 Reorder the terms: 7xy2 + 7x2y2 + 6x3y2 + (-3xy2 + -3x2y2 + 6x3y2) = 0 Remove parenthesis around (-3xy2 + -3x2y2 + 6x3y2) 7xy2 + 7x2y2 + 6x3y2 + -3xy2 + -3x2y2 + 6x3y2 = 0 Reorder the terms: 7xy2 + -3xy2 + 7x2y2 + -3x2y2 + 6x3y2 + 6x3y2 = 0 Combine like terms: 7xy2 + -3xy2 = 4xy2 4xy2 + 7x2y2 + -3x2y2 + 6x3y2 + 6x3y2 = 0 Combine like terms: 7x2y2 + -3x2y2 = 4x2y2 4xy2 + 4x2y2 + 6x3y2 + 6x3y2 = 0 Combine like terms: 6x3y2 + 6x3y2 = 12x3y2 4xy2 + 4x2y2 + 12x3y2 = 0 Solving 4xy2 + 4x2y2 + 12x3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4xy2'. 4xy2(1 + x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve: Simplifying xy2 = 0 Solving xy2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy2 = 0 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 '(1 + x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + x + 3x2 = 0 Solving 1 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.3333333333x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.3333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + -0.3333333333 0.3333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.3333333333x + x2 = -0.3333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.3333333333x + x2 = -0.0833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0833333333 Can't calculate square root of the right side. 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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