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Simplifying 3X3 + 8X2 + -24X = 0 Reorder the terms: -24X + 8X2 + 3X3 = 0 Solving -24X + 8X2 + 3X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-24 + 8X + 3X2) = 0Subproblem 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 '(-24 + 8X + 3X2)' equal to zero and attempt to solve: Simplifying -24 + 8X + 3X2 = 0 Solving -24 + 8X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 2.666666667X + X2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.666666667X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + 2.666666667X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.666666667X + X2 = 0 + 8 2.666666667X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.666666667X + X2 = 8 The X term is 2.666666667X. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667X + 1.777777780 + X2 = 8 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667X + X2 = 8 + 1.777777780 Combine like terms: 8 + 1.777777780 = 9.77777778 1.777777780 + 2.666666667X + X2 = 9.77777778 Factor a perfect square on the left side: (X + 1.333333334)(X + 1.333333334) = 9.77777778 Calculate the square root of the right side: 3.12694384 Break this problem into two subproblems by setting (X + 1.333333334) equal to 3.12694384 and -3.12694384.Subproblem 1
X + 1.333333334 = 3.12694384 Simplifying X + 1.333333334 = 3.12694384 Reorder the terms: 1.333333334 + X = 3.12694384 Solving 1.333333334 + X = 3.12694384 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + X = 3.12694384 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + X = 3.12694384 + -1.333333334 X = 3.12694384 + -1.333333334 Combine like terms: 3.12694384 + -1.333333334 = 1.793610506 X = 1.793610506 Simplifying X = 1.793610506Subproblem 2
X + 1.333333334 = -3.12694384 Simplifying X + 1.333333334 = -3.12694384 Reorder the terms: 1.333333334 + X = -3.12694384 Solving 1.333333334 + X = -3.12694384 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + X = -3.12694384 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + X = -3.12694384 + -1.333333334 X = -3.12694384 + -1.333333334 Combine like terms: -3.12694384 + -1.333333334 = -4.460277174 X = -4.460277174 Simplifying X = -4.460277174Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.793610506, -4.460277174}Solution
X = {0, 1.793610506, -4.460277174}
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