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Simplifying 3x5 + -1x4 + 2x3 = 0 Reorder the terms: 2x3 + -1x4 + 3x5 = 0 Solving 2x3 + -1x4 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(2 + -1x + 3x2) = 0Subproblem 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 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + 3x2 = 0 Solving 2 + -1x + 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 -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -0.6666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -0.6666666667 + 0.02777777779 Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891 0.02777777779 + -0.3333333333x + x2 = -0.63888888891 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.63888888891 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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