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Simplifying (4x + -3)(2x + -5) = 16x Reorder the terms: (-3 + 4x)(2x + -5) = 16x Reorder the terms: (-3 + 4x)(-5 + 2x) = 16x Multiply (-3 + 4x) * (-5 + 2x) (-3(-5 + 2x) + 4x * (-5 + 2x)) = 16x ((-5 * -3 + 2x * -3) + 4x * (-5 + 2x)) = 16x ((15 + -6x) + 4x * (-5 + 2x)) = 16x (15 + -6x + (-5 * 4x + 2x * 4x)) = 16x (15 + -6x + (-20x + 8x2)) = 16x Combine like terms: -6x + -20x = -26x (15 + -26x + 8x2) = 16x Solving 15 + -26x + 8x2 = 16x Solving for variable 'x'. Reorder the terms: 15 + -26x + -16x + 8x2 = 16x + -16x Combine like terms: -26x + -16x = -42x 15 + -42x + 8x2 = 16x + -16x Combine like terms: 16x + -16x = 0 15 + -42x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -5.25x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -5.25x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -5.25x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -5.25x + x2 = 0 + -1.875 -5.25x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -5.25x + x2 = -1.875 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -1.875 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -1.875 + 6.890625 Combine like terms: -1.875 + 6.890625 = 5.015625 6.890625 + -5.25x + x2 = 5.015625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (x + -2.625) equal to 2.239559108 and -2.239559108.Subproblem 1
x + -2.625 = 2.239559108 Simplifying x + -2.625 = 2.239559108 Reorder the terms: -2.625 + x = 2.239559108 Solving -2.625 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.239559108 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.239559108 + 2.625 x = 2.239559108 + 2.625 Combine like terms: 2.239559108 + 2.625 = 4.864559108 x = 4.864559108 Simplifying x = 4.864559108Subproblem 2
x + -2.625 = -2.239559108 Simplifying x + -2.625 = -2.239559108 Reorder the terms: -2.625 + x = -2.239559108 Solving -2.625 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.239559108 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.239559108 + 2.625 x = -2.239559108 + 2.625 Combine like terms: -2.239559108 + 2.625 = 0.385440892 x = 0.385440892 Simplifying x = 0.385440892Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.864559108, 0.385440892}
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