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Simplifying 2x(5x2 + -3x + 3) = 0 Reorder the terms: 2x(3 + -3x + 5x2) = 0 (3 * 2x + -3x * 2x + 5x2 * 2x) = 0 (6x + -6x2 + 10x3) = 0 Solving 6x + -6x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -3x + 5x2) = 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 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + -3x + 5x2 = 0 Solving 3 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -0.6x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -0.6x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -0.6x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -0.6x + x2 = 0 + -0.6 -0.6x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -0.6x + x2 = -0.6 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 = -0.6 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -0.6 + 0.09 Combine like terms: -0.6 + 0.09 = -0.51 0.09 + -0.6x + x2 = -0.51 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -0.51 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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