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Simplifying (8 + (x + 4)) * 8 = (x + 2x) * x Reorder the terms: (8 + (4 + x)) * 8 = (x + 2x) * x Remove parenthesis around (4 + x) (8 + 4 + x) * 8 = (x + 2x) * x Combine like terms: 8 + 4 = 12 (12 + x) * 8 = (x + 2x) * x Reorder the terms for easier multiplication: 8(12 + x) = (x + 2x) * x (12 * 8 + x * 8) = (x + 2x) * x (96 + 8x) = (x + 2x) * x Combine like terms: x + 2x = 3x 96 + 8x = (3x) * x Remove parenthesis around (3x) 96 + 8x = 3x * x Multiply x * x 96 + 8x = 3x2 Solving 96 + 8x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 96 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -32 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -2.666666667x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -2.666666667x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -2.666666667x + x2 = 0 + 32 -2.666666667x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -2.666666667x + x2 = 32 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 = 32 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 32 + 1.777777780 Combine like terms: 32 + 1.777777780 = 33.77777778 1.777777780 + -2.666666667x + x2 = 33.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 33.77777778 Calculate the square root of the right side: 5.811865258 Break this problem into two subproblems by setting (x + -1.333333334) equal to 5.811865258 and -5.811865258.Subproblem 1
x + -1.333333334 = 5.811865258 Simplifying x + -1.333333334 = 5.811865258 Reorder the terms: -1.333333334 + x = 5.811865258 Solving -1.333333334 + x = 5.811865258 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 = 5.811865258 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 5.811865258 + 1.333333334 x = 5.811865258 + 1.333333334 Combine like terms: 5.811865258 + 1.333333334 = 7.145198592 x = 7.145198592 Simplifying x = 7.145198592Subproblem 2
x + -1.333333334 = -5.811865258 Simplifying x + -1.333333334 = -5.811865258 Reorder the terms: -1.333333334 + x = -5.811865258 Solving -1.333333334 + x = -5.811865258 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 = -5.811865258 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -5.811865258 + 1.333333334 x = -5.811865258 + 1.333333334 Combine like terms: -5.811865258 + 1.333333334 = -4.478531924 x = -4.478531924 Simplifying x = -4.478531924Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.145198592, -4.478531924}
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