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Simplifying 0.75x(16 + -8x) = 5x + -9 (16 * 0.75x + -8x * 0.75x) = 5x + -9 (12x + -6x2) = 5x + -9 Reorder the terms: 12x + -6x2 = -9 + 5x Solving 12x + -6x2 = -9 + 5x Solving for variable 'x'. Reorder the terms: 9 + 12x + -5x + -6x2 = -9 + 5x + 9 + -5x Combine like terms: 12x + -5x = 7x 9 + 7x + -6x2 = -9 + 5x + 9 + -5x Reorder the terms: 9 + 7x + -6x2 = -9 + 9 + 5x + -5x Combine like terms: -9 + 9 = 0 9 + 7x + -6x2 = 0 + 5x + -5x 9 + 7x + -6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 9 + 7x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.166666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.166666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.166666667x + x2 = 0 + 1.5 -1.166666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.166666667x + x2 = 1.5 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 1.5 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 1.5 + 0.3402777780 Combine like terms: 1.5 + 0.3402777780 = 1.840277778 0.3402777780 + -1.166666667x + x2 = 1.840277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.840277778 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.356568383 and -1.356568383.Subproblem 1
x + -0.5833333335 = 1.356568383 Simplifying x + -0.5833333335 = 1.356568383 Reorder the terms: -0.5833333335 + x = 1.356568383 Solving -0.5833333335 + x = 1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 1.356568383 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.356568383 + 0.5833333335 x = 1.356568383 + 0.5833333335 Combine like terms: 1.356568383 + 0.5833333335 = 1.9399017165 x = 1.9399017165 Simplifying x = 1.9399017165Subproblem 2
x + -0.5833333335 = -1.356568383 Simplifying x + -0.5833333335 = -1.356568383 Reorder the terms: -0.5833333335 + x = -1.356568383 Solving -0.5833333335 + x = -1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -1.356568383 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.356568383 + 0.5833333335 x = -1.356568383 + 0.5833333335 Combine like terms: -1.356568383 + 0.5833333335 = -0.7732350495 x = -0.7732350495 Simplifying x = -0.7732350495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9399017165, -0.7732350495}
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