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Simplifying 3x2 + 8x + -384 = 0 Reorder the terms: -384 + 8x + 3x2 = 0 Solving -384 + 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'. -128 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 2.666666667x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 2.666666667x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 2.666666667x + x2 = 0 + 128 2.666666667x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 2.666666667x + x2 = 128 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 = 128 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 128 + 1.777777780 Combine like terms: 128 + 1.777777780 = 129.77777778 1.777777780 + 2.666666667x + x2 = 129.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 129.77777778 Calculate the square root of the right side: 11.392004994 Break this problem into two subproblems by setting (x + 1.333333334) equal to 11.392004994 and -11.392004994.Subproblem 1
x + 1.333333334 = 11.392004994 Simplifying x + 1.333333334 = 11.392004994 Reorder the terms: 1.333333334 + x = 11.392004994 Solving 1.333333334 + x = 11.392004994 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 = 11.392004994 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 11.392004994 + -1.333333334 x = 11.392004994 + -1.333333334 Combine like terms: 11.392004994 + -1.333333334 = 10.05867166 x = 10.05867166 Simplifying x = 10.05867166Subproblem 2
x + 1.333333334 = -11.392004994 Simplifying x + 1.333333334 = -11.392004994 Reorder the terms: 1.333333334 + x = -11.392004994 Solving 1.333333334 + x = -11.392004994 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 = -11.392004994 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -11.392004994 + -1.333333334 x = -11.392004994 + -1.333333334 Combine like terms: -11.392004994 + -1.333333334 = -12.725338328 x = -12.725338328 Simplifying x = -12.725338328Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.05867166, -12.725338328}
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