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Simplifying 45x + -10x2 + 15x3 = 0 Solving 45x + -10x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(9 + -2x + 3x2) = 0 Ignore the factor 5.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 '(9 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 9 + -2x + 3x2 = 0 Solving 9 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -0.6666666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -0.6666666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -0.6666666667x + x2 = 0 + -3 -0.6666666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -0.6666666667x + x2 = -3 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -3 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -3 + 0.1111111112 Combine like terms: -3 + 0.1111111112 = -2.8888888888 0.1111111112 + -0.6666666667x + x2 = -2.8888888888 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -2.8888888888 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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