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Simplifying 3x(5x2 + -3x + 4) = 0 Reorder the terms: 3x(4 + -3x + 5x2) = 0 (4 * 3x + -3x * 3x + 5x2 * 3x) = 0 (12x + -9x2 + 15x3) = 0 Solving 12x + -9x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(4 + -3x + 5x2) = 0 Ignore the factor 3.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 '(4 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + 5x2 = 0 Solving 4 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -0.6x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -0.6x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -0.6x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -0.6x + x2 = 0 + -0.8 -0.6x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -0.6x + x2 = -0.8 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -0.8 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -0.8 + 0.09 Combine like terms: -0.8 + 0.09 = -0.71 0.09 + -0.6x + x2 = -0.71 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -0.71 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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