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Simplifying 2x(3x2 + -6x + 1) = 0 Reorder the terms: 2x(1 + -6x + 3x2) = 0 (1 * 2x + -6x * 2x + 3x2 * 2x) = 0 (2x + -12x2 + 6x3) = 0 Solving 2x + -12x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + -6x + 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 '(1 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -6x + 3x2 = 0 Solving 1 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -2x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -2x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.3333333333 -2x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -2x + x2 = -0.3333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.3333333333 + 1 Reorder the terms: 1 + -2x + x2 = -0.3333333333 + 1 Combine like terms: -0.3333333333 + 1 = 0.6666666667 1 + -2x + x2 = 0.6666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.6666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + -1) equal to 0.816496581 and -0.816496581.Subproblem 1
x + -1 = 0.816496581 Simplifying x + -1 = 0.816496581 Reorder the terms: -1 + x = 0.816496581 Solving -1 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.816496581 + 1 x = 0.816496581 + 1 Combine like terms: 0.816496581 + 1 = 1.816496581 x = 1.816496581 Simplifying x = 1.816496581Subproblem 2
x + -1 = -0.816496581 Simplifying x + -1 = -0.816496581 Reorder the terms: -1 + x = -0.816496581 Solving -1 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.816496581 + 1 x = -0.816496581 + 1 Combine like terms: -0.816496581 + 1 = 0.183503419 x = 0.183503419 Simplifying x = 0.183503419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.816496581, 0.183503419}Solution
x = {0, 1.816496581, 0.183503419}
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