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Simplifying -6x3 + -10x2 + -6x = 0 Reorder the terms: -6x + -10x2 + -6x3 = 0 Solving -6x + -10x2 + -6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2x'. -2x(3 + 5x + 3x2) = 0 Ignore the factor -2.Subproblem 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 '(3 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 5x + 3x2 = 0 Solving 3 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.666666667x + x2 = 0 + -1 1.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.666666667x + x2 = -1 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -1 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -1 + 0.6944444447 Combine like terms: -1 + 0.6944444447 = -0.3055555553 0.6944444447 + 1.666666667x + x2 = -0.3055555553 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -0.3055555553 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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