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Simplifying (2x + -1)(x + 6) = 148 Reorder the terms: (-1 + 2x)(x + 6) = 148 Reorder the terms: (-1 + 2x)(6 + x) = 148 Multiply (-1 + 2x) * (6 + x) (-1(6 + x) + 2x * (6 + x)) = 148 ((6 * -1 + x * -1) + 2x * (6 + x)) = 148 ((-6 + -1x) + 2x * (6 + x)) = 148 (-6 + -1x + (6 * 2x + x * 2x)) = 148 (-6 + -1x + (12x + 2x2)) = 148 Combine like terms: -1x + 12x = 11x (-6 + 11x + 2x2) = 148 Solving -6 + 11x + 2x2 = 148 Solving for variable 'x'. Reorder the terms: -6 + -148 + 11x + 2x2 = 148 + -148 Combine like terms: -6 + -148 = -154 -154 + 11x + 2x2 = 148 + -148 Combine like terms: 148 + -148 = 0 -154 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77 + 5.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 5.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 5.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 5.5x + x2 = 0 + 77 5.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 5.5x + x2 = 77 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 = 77 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 77 + 7.5625 Combine like terms: 77 + 7.5625 = 84.5625 7.5625 + 5.5x + x2 = 84.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 84.5625 Calculate the square root of the right side: 9.195787079 Break this problem into two subproblems by setting (x + 2.75) equal to 9.195787079 and -9.195787079.Subproblem 1
x + 2.75 = 9.195787079 Simplifying x + 2.75 = 9.195787079 Reorder the terms: 2.75 + x = 9.195787079 Solving 2.75 + x = 9.195787079 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 = 9.195787079 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 9.195787079 + -2.75 x = 9.195787079 + -2.75 Combine like terms: 9.195787079 + -2.75 = 6.445787079 x = 6.445787079 Simplifying x = 6.445787079Subproblem 2
x + 2.75 = -9.195787079 Simplifying x + 2.75 = -9.195787079 Reorder the terms: 2.75 + x = -9.195787079 Solving 2.75 + x = -9.195787079 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 = -9.195787079 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -9.195787079 + -2.75 x = -9.195787079 + -2.75 Combine like terms: -9.195787079 + -2.75 = -11.945787079 x = -11.945787079 Simplifying x = -11.945787079Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.445787079, -11.945787079}
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