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Simplifying 3x5 + -10x3 + 23x = 0 Reorder the terms: 23x + -10x3 + 3x5 = 0 Solving 23x + -10x3 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(23 + -10x2 + 3x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(23 + -10x2 + 3x4)' equal to zero and attempt to solve: Simplifying 23 + -10x2 + 3x4 = 0 Solving 23 + -10x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.666666667 + -3.333333333x2 + x4 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + -3.333333333x2 + -7.666666667 + x4 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + -3.333333333x2 + x4 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + -3.333333333x2 + x4 = 0 + -7.666666667 -3.333333333x2 + x4 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 -3.333333333x2 + x4 = -7.666666667 The x term is -3.333333333x2. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x2 + 2.777777779 + x4 = -7.666666667 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x2 + x4 = -7.666666667 + 2.777777779 Combine like terms: -7.666666667 + 2.777777779 = -4.888888888 2.777777779 + -3.333333333x2 + x4 = -4.888888888 Factor a perfect square on the left side: (x2 + -1.666666667)(x2 + -1.666666667) = -4.888888888 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.Solution
x = {0}
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