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Simplifying 3xy(3x2 + 6x + 10) = 0 Reorder the terms: 3xy(10 + 6x + 3x2) = 0 (10 * 3xy + 6x * 3xy + 3x2 * 3xy) = 0 (30xy + 18x2y + 9x3y) = 0 Solving 30xy + 18x2y + 9x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3xy'. 3xy(10 + 6x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 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 '(10 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + 6x + 3x2 = 0 Solving 10 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 2x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 2x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + -3.333333333 2x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 2x + x2 = -3.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -3.333333333 + 1 Reorder the terms: 1 + 2x + x2 = -3.333333333 + 1 Combine like terms: -3.333333333 + 1 = -2.333333333 1 + 2x + x2 = -2.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = -2.333333333 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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