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Simplifying 2.4x(x + -6) = -5.6x + 8 Reorder the terms: 2.4x(-6 + x) = -5.6x + 8 (-6 * 2.4x + x * 2.4x) = -5.6x + 8 (-14.4x + 2.4x2) = -5.6x + 8 Reorder the terms: -14.4x + 2.4x2 = 8 + -5.6x Solving -14.4x + 2.4x2 = 8 + -5.6x Solving for variable 'x'. Reorder the terms: -8 + -14.4x + 5.6x + 2.4x2 = 8 + -5.6x + -8 + 5.6x Combine like terms: -14.4x + 5.6x = -8.8x -8 + -8.8x + 2.4x2 = 8 + -5.6x + -8 + 5.6x Reorder the terms: -8 + -8.8x + 2.4x2 = 8 + -8 + -5.6x + 5.6x Combine like terms: 8 + -8 = 0 -8 + -8.8x + 2.4x2 = 0 + -5.6x + 5.6x -8 + -8.8x + 2.4x2 = -5.6x + 5.6x Combine like terms: -5.6x + 5.6x = 0.0 -8 + -8.8x + 2.4x2 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -3.333333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -3.666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -3.666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 3.333333333 -3.666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -3.666666667x + x2 = 3.333333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 3.333333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 3.333333333 + 3.361111114 Combine like terms: 3.333333333 + 3.361111114 = 6.694444447 3.361111114 + -3.666666667x + x2 = 6.694444447 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 6.694444447 Calculate the square root of the right side: 2.58736245 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.58736245 and -2.58736245.Subproblem 1
x + -1.833333334 = 2.58736245 Simplifying x + -1.833333334 = 2.58736245 Reorder the terms: -1.833333334 + x = 2.58736245 Solving -1.833333334 + x = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.58736245 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.58736245 + 1.833333334 x = 2.58736245 + 1.833333334 Combine like terms: 2.58736245 + 1.833333334 = 4.420695784 x = 4.420695784 Simplifying x = 4.420695784Subproblem 2
x + -1.833333334 = -2.58736245 Simplifying x + -1.833333334 = -2.58736245 Reorder the terms: -1.833333334 + x = -2.58736245 Solving -1.833333334 + x = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.58736245 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.58736245 + 1.833333334 x = -2.58736245 + 1.833333334 Combine like terms: -2.58736245 + 1.833333334 = -0.754029116 x = -0.754029116 Simplifying x = -0.754029116Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.420695784, -0.754029116}
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