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Simplifying -3x(4 + -1x) = 10 + -26 + 5x (4 * -3x + -1x * -3x) = 10 + -26 + 5x (-12x + 3x2) = 10 + -26 + 5x Combine like terms: 10 + -26 = -16 -12x + 3x2 = -16 + 5x Solving -12x + 3x2 = -16 + 5x Solving for variable 'x'. Reorder the terms: 16 + -12x + -5x + 3x2 = -16 + 5x + 16 + -5x Combine like terms: -12x + -5x = -17x 16 + -17x + 3x2 = -16 + 5x + 16 + -5x Reorder the terms: 16 + -17x + 3x2 = -16 + 16 + 5x + -5x Combine like terms: -16 + 16 = 0 16 + -17x + 3x2 = 0 + 5x + -5x 16 + -17x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 16 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -5.666666667x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -5.666666667x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + -5.333333333 -5.666666667x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -5.666666667x + x2 = -5.333333333 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = -5.333333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -5.333333333 + 8.027777782 Combine like terms: -5.333333333 + 8.027777782 = 2.694444449 8.027777782 + -5.666666667x + x2 = 2.694444449 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 2.694444449 Calculate the square root of the right side: 1.641476302 Break this problem into two subproblems by setting (x + -2.833333334) equal to 1.641476302 and -1.641476302.Subproblem 1
x + -2.833333334 = 1.641476302 Simplifying x + -2.833333334 = 1.641476302 Reorder the terms: -2.833333334 + x = 1.641476302 Solving -2.833333334 + x = 1.641476302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 1.641476302 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 1.641476302 + 2.833333334 x = 1.641476302 + 2.833333334 Combine like terms: 1.641476302 + 2.833333334 = 4.474809636 x = 4.474809636 Simplifying x = 4.474809636Subproblem 2
x + -2.833333334 = -1.641476302 Simplifying x + -2.833333334 = -1.641476302 Reorder the terms: -2.833333334 + x = -1.641476302 Solving -2.833333334 + x = -1.641476302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -1.641476302 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -1.641476302 + 2.833333334 x = -1.641476302 + 2.833333334 Combine like terms: -1.641476302 + 2.833333334 = 1.191857032 x = 1.191857032 Simplifying x = 1.191857032Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.474809636, 1.191857032}
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