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Simplifying (x + 8)(4 + -1x) = (2x + -1) Reorder the terms: (8 + x)(4 + -1x) = (2x + -1) Multiply (8 + x) * (4 + -1x) (8(4 + -1x) + x(4 + -1x)) = (2x + -1) ((4 * 8 + -1x * 8) + x(4 + -1x)) = (2x + -1) ((32 + -8x) + x(4 + -1x)) = (2x + -1) (32 + -8x + (4 * x + -1x * x)) = (2x + -1) (32 + -8x + (4x + -1x2)) = (2x + -1) Combine like terms: -8x + 4x = -4x (32 + -4x + -1x2) = (2x + -1) Reorder the terms: 32 + -4x + -1x2 = (-1 + 2x) Remove parenthesis around (-1 + 2x) 32 + -4x + -1x2 = -1 + 2x Solving 32 + -4x + -1x2 = -1 + 2x Solving for variable 'x'. Reorder the terms: 32 + 1 + -4x + -2x + -1x2 = -1 + 2x + 1 + -2x Combine like terms: 32 + 1 = 33 33 + -4x + -2x + -1x2 = -1 + 2x + 1 + -2x Combine like terms: -4x + -2x = -6x 33 + -6x + -1x2 = -1 + 2x + 1 + -2x Reorder the terms: 33 + -6x + -1x2 = -1 + 1 + 2x + -2x Combine like terms: -1 + 1 = 0 33 + -6x + -1x2 = 0 + 2x + -2x 33 + -6x + -1x2 = 2x + -2x Combine like terms: 2x + -2x = 0 33 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + 6x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 6x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 6x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 6x + x2 = 0 + 33 6x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 6x + x2 = 33 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 33 + 9 Reorder the terms: 9 + 6x + x2 = 33 + 9 Combine like terms: 33 + 9 = 42 9 + 6x + x2 = 42 Factor a perfect square on the left side: (x + 3)(x + 3) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 3) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 3 = 6.480740698 Simplifying x + 3 = 6.480740698 Reorder the terms: 3 + x = 6.480740698 Solving 3 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.480740698 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.480740698 + -3 x = 6.480740698 + -3 Combine like terms: 6.480740698 + -3 = 3.480740698 x = 3.480740698 Simplifying x = 3.480740698Subproblem 2
x + 3 = -6.480740698 Simplifying x + 3 = -6.480740698 Reorder the terms: 3 + x = -6.480740698 Solving 3 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.480740698 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.480740698 + -3 x = -6.480740698 + -3 Combine like terms: -6.480740698 + -3 = -9.480740698 x = -9.480740698 Simplifying x = -9.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.480740698, -9.480740698}
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