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Simplifying x(3x + -8) = 48 Reorder the terms: x(-8 + 3x) = 48 (-8 * x + 3x * x) = 48 (-8x + 3x2) = 48 Solving -8x + 3x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -8x + 3x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -2.666666667x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -2.666666667x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2.666666667x + x2 = 0 + 16 -2.666666667x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2.666666667x + x2 = 16 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 = 16 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 16 + 1.777777780 Combine like terms: 16 + 1.777777780 = 17.77777778 1.777777780 + -2.666666667x + x2 = 17.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 17.77777778 Calculate the square root of the right side: 4.216370214 Break this problem into two subproblems by setting (x + -1.333333334) equal to 4.216370214 and -4.216370214.Subproblem 1
x + -1.333333334 = 4.216370214 Simplifying x + -1.333333334 = 4.216370214 Reorder the terms: -1.333333334 + x = 4.216370214 Solving -1.333333334 + x = 4.216370214 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 = 4.216370214 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 4.216370214 + 1.333333334 x = 4.216370214 + 1.333333334 Combine like terms: 4.216370214 + 1.333333334 = 5.549703548 x = 5.549703548 Simplifying x = 5.549703548Subproblem 2
x + -1.333333334 = -4.216370214 Simplifying x + -1.333333334 = -4.216370214 Reorder the terms: -1.333333334 + x = -4.216370214 Solving -1.333333334 + x = -4.216370214 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 = -4.216370214 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -4.216370214 + 1.333333334 x = -4.216370214 + 1.333333334 Combine like terms: -4.216370214 + 1.333333334 = -2.88303688 x = -2.88303688 Simplifying x = -2.88303688Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.549703548, -2.88303688}
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