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Simplifying -1x4 + 13x5 + 6x3 + 6x3 + 5x5 + 7x4 = 0 Reorder the terms: 6x3 + 6x3 + -1x4 + 7x4 + 13x5 + 5x5 = 0 Combine like terms: 6x3 + 6x3 = 12x3 12x3 + -1x4 + 7x4 + 13x5 + 5x5 = 0 Combine like terms: -1x4 + 7x4 = 6x4 12x3 + 6x4 + 13x5 + 5x5 = 0 Combine like terms: 13x5 + 5x5 = 18x5 12x3 + 6x4 + 18x5 = 0 Solving 12x3 + 6x4 + 18x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x3'. 6x3(2 + x + 3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(2 + x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + x + 3x2 = 0 Solving 2 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.3333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + -0.6666666667 0.3333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.3333333333x + x2 = -0.6666666667 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 = -0.6666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 0.25 + 0.3333333333x + x2 = -0.4166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.4166666667 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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