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Simplifying (2x + -3)(x + -4) = 6 Reorder the terms: (-3 + 2x)(x + -4) = 6 Reorder the terms: (-3 + 2x)(-4 + x) = 6 Multiply (-3 + 2x) * (-4 + x) (-3(-4 + x) + 2x * (-4 + x)) = 6 ((-4 * -3 + x * -3) + 2x * (-4 + x)) = 6 ((12 + -3x) + 2x * (-4 + x)) = 6 (12 + -3x + (-4 * 2x + x * 2x)) = 6 (12 + -3x + (-8x + 2x2)) = 6 Combine like terms: -3x + -8x = -11x (12 + -11x + 2x2) = 6 Solving 12 + -11x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: 12 + -6 + -11x + 2x2 = 6 + -6 Combine like terms: 12 + -6 = 6 6 + -11x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 6 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -5.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.5x + x2 = 0 + -3 -5.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.5x + x2 = -3 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -3 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + -5.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -2.75 = 2.136000936 Simplifying x + -2.75 = 2.136000936 Reorder the terms: -2.75 + x = 2.136000936 Solving -2.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.136000936 + 2.75 x = 2.136000936 + 2.75 Combine like terms: 2.136000936 + 2.75 = 4.886000936 x = 4.886000936 Simplifying x = 4.886000936Subproblem 2
x + -2.75 = -2.136000936 Simplifying x + -2.75 = -2.136000936 Reorder the terms: -2.75 + x = -2.136000936 Solving -2.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.136000936 + 2.75 x = -2.136000936 + 2.75 Combine like terms: -2.136000936 + 2.75 = 0.613999064 x = 0.613999064 Simplifying x = 0.613999064Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.886000936, 0.613999064}
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