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Simplifying 3X2 + -8X + -24 = 0 Reorder the terms: -24 + -8X + 3X2 = 0 Solving -24 + -8X + 3X2 = 0 Solving for variable 'X'. 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 = 4.460277174 X = 4.460277174 Simplifying X = 4.460277174Subproblem 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 = -1.793610506 X = -1.793610506 Simplifying X = -1.793610506Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.460277174, -1.793610506}
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