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Simplifying 3(-6x + 7) * 4x = -7 Reorder the terms: 3(7 + -6x) * 4x = -7 Reorder the terms for easier multiplication: 3 * 4x(7 + -6x) = -7 Multiply 3 * 4 12x(7 + -6x) = -7 (7 * 12x + -6x * 12x) = -7 (84x + -72x2) = -7 Solving 84x + -72x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 84x + -72x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 84x + -72x2 = 0 Begin completing the square. Divide all terms by -72 the coefficient of the squared term: Divide each side by '-72'. -0.09722222222 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.09722222222' to each side of the equation. -0.09722222222 + -1.166666667x + 0.09722222222 + x2 = 0 + 0.09722222222 Reorder the terms: -0.09722222222 + 0.09722222222 + -1.166666667x + x2 = 0 + 0.09722222222 Combine like terms: -0.09722222222 + 0.09722222222 = 0.00000000000 0.00000000000 + -1.166666667x + x2 = 0 + 0.09722222222 -1.166666667x + x2 = 0 + 0.09722222222 Combine like terms: 0 + 0.09722222222 = 0.09722222222 -1.166666667x + x2 = 0.09722222222 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 = 0.09722222222 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.09722222222 + 0.3402777780 Combine like terms: 0.09722222222 + 0.3402777780 = 0.43750000022 0.3402777780 + -1.166666667x + x2 = 0.43750000022 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.43750000022 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.661437828 and -0.661437828.Subproblem 1
x + -0.5833333335 = 0.661437828 Simplifying x + -0.5833333335 = 0.661437828 Reorder the terms: -0.5833333335 + x = 0.661437828 Solving -0.5833333335 + x = 0.661437828 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 = 0.661437828 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.661437828 + 0.5833333335 x = 0.661437828 + 0.5833333335 Combine like terms: 0.661437828 + 0.5833333335 = 1.2447711615 x = 1.2447711615 Simplifying x = 1.2447711615Subproblem 2
x + -0.5833333335 = -0.661437828 Simplifying x + -0.5833333335 = -0.661437828 Reorder the terms: -0.5833333335 + x = -0.661437828 Solving -0.5833333335 + x = -0.661437828 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 = -0.661437828 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.661437828 + 0.5833333335 x = -0.661437828 + 0.5833333335 Combine like terms: -0.661437828 + 0.5833333335 = -0.0781044945 x = -0.0781044945 Simplifying x = -0.0781044945Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2447711615, -0.0781044945}
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