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Simplifying 3X(6 + -1X) + 2X = 24 (6 * 3X + -1X * 3X) + 2X = 24 (18X + -3X2) + 2X = 24 Reorder the terms: 18X + 2X + -3X2 = 24 Combine like terms: 18X + 2X = 20X 20X + -3X2 = 24 Solving 20X + -3X2 = 24 Solving for variable 'X'. Reorder the terms: -24 + 20X + -3X2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 20X + -3X2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 8 + -6.666666667X + X2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6.666666667X + -8 + X2 = 0 + -8 Reorder the terms: 8 + -8 + -6.666666667X + X2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6.666666667X + X2 = 0 + -8 -6.666666667X + X2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6.666666667X + X2 = -8 The X term is -6.666666667X. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667X + 11.11111112 + X2 = -8 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667X + X2 = -8 + 11.11111112 Combine like terms: -8 + 11.11111112 = 3.11111112 11.11111112 + -6.666666667X + X2 = 3.11111112 Factor a perfect square on the left side: (X + -3.333333334)(X + -3.333333334) = 3.11111112 Calculate the square root of the right side: 1.76383421 Break this problem into two subproblems by setting (X + -3.333333334) equal to 1.76383421 and -1.76383421.Subproblem 1
X + -3.333333334 = 1.76383421 Simplifying X + -3.333333334 = 1.76383421 Reorder the terms: -3.333333334 + X = 1.76383421 Solving -3.333333334 + X = 1.76383421 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + X = 1.76383421 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + X = 1.76383421 + 3.333333334 X = 1.76383421 + 3.333333334 Combine like terms: 1.76383421 + 3.333333334 = 5.097167544 X = 5.097167544 Simplifying X = 5.097167544Subproblem 2
X + -3.333333334 = -1.76383421 Simplifying X + -3.333333334 = -1.76383421 Reorder the terms: -3.333333334 + X = -1.76383421 Solving -3.333333334 + X = -1.76383421 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + X = -1.76383421 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + X = -1.76383421 + 3.333333334 X = -1.76383421 + 3.333333334 Combine like terms: -1.76383421 + 3.333333334 = 1.569499124 X = 1.569499124 Simplifying X = 1.569499124Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.097167544, 1.569499124}
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