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Simplifying 3x(6x2 + -12x) + -8(4x + -3x2) = 0 Reorder the terms: 3x(-12x + 6x2) + -8(4x + -3x2) = 0 (-12x * 3x + 6x2 * 3x) + -8(4x + -3x2) = 0 (-36x2 + 18x3) + -8(4x + -3x2) = 0 -36x2 + 18x3 + (4x * -8 + -3x2 * -8) = 0 -36x2 + 18x3 + (-32x + 24x2) = 0 Reorder the terms: -32x + -36x2 + 24x2 + 18x3 = 0 Combine like terms: -36x2 + 24x2 = -12x2 -32x + -12x2 + 18x3 = 0 Solving -32x + -12x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-16 + -6x + 9x2) = 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 '(-16 + -6x + 9x2)' equal to zero and attempt to solve: Simplifying -16 + -6x + 9x2 = 0 Solving -16 + -6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.6666666667x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.6666666667x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 1.777777778 -0.6666666667x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.6666666667x + x2 = 1.777777778 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 = 1.777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 1.777777778 + 0.1111111112 Combine like terms: 1.777777778 + 0.1111111112 = 1.8888888892 0.1111111112 + -0.6666666667x + x2 = 1.8888888892 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 1.8888888892 Calculate the square root of the right side: 1.374368542 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.374368542 and -1.374368542.Subproblem 1
x + -0.3333333334 = 1.374368542 Simplifying x + -0.3333333334 = 1.374368542 Reorder the terms: -0.3333333334 + x = 1.374368542 Solving -0.3333333334 + x = 1.374368542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.374368542 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.374368542 + 0.3333333334 x = 1.374368542 + 0.3333333334 Combine like terms: 1.374368542 + 0.3333333334 = 1.7077018754 x = 1.7077018754 Simplifying x = 1.7077018754Subproblem 2
x + -0.3333333334 = -1.374368542 Simplifying x + -0.3333333334 = -1.374368542 Reorder the terms: -0.3333333334 + x = -1.374368542 Solving -0.3333333334 + x = -1.374368542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.374368542 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.374368542 + 0.3333333334 x = -1.374368542 + 0.3333333334 Combine like terms: -1.374368542 + 0.3333333334 = -1.0410352086 x = -1.0410352086 Simplifying x = -1.0410352086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7077018754, -1.0410352086}Solution
x = {0, 1.7077018754, -1.0410352086}
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