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Simplifying 15x3 + 20x2 + 10x = 0 Reorder the terms: 10x + 20x2 + 15x3 = 0 Solving 10x + 20x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(2 + 4x + 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 '(2 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + 3x2 = 0 Solving 2 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 1.333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 1.333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.6666666667 1.333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 1.333333333x + x2 = -0.6666666667 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.6666666667 + 0.4444444442 Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225 0.4444444442 + 1.333333333x + x2 = -0.2222222225 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -0.2222222225 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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