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Simplifying -16x2 + -43x + 242 = 0 Reorder the terms: 242 + -43x + -16x2 = 0 Solving 242 + -43x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -15.125 + 2.6875x + x2 = 0 Move the constant term to the right: Add '15.125' to each side of the equation. -15.125 + 2.6875x + 15.125 + x2 = 0 + 15.125 Reorder the terms: -15.125 + 15.125 + 2.6875x + x2 = 0 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + 2.6875x + x2 = 0 + 15.125 2.6875x + x2 = 0 + 15.125 Combine like terms: 0 + 15.125 = 15.125 2.6875x + x2 = 15.125 The x term is 2.6875x. Take half its coefficient (1.34375). Square it (1.805664063) and add it to both sides. Add '1.805664063' to each side of the equation. 2.6875x + 1.805664063 + x2 = 15.125 + 1.805664063 Reorder the terms: 1.805664063 + 2.6875x + x2 = 15.125 + 1.805664063 Combine like terms: 15.125 + 1.805664063 = 16.930664063 1.805664063 + 2.6875x + x2 = 16.930664063 Factor a perfect square on the left side: (x + 1.34375)(x + 1.34375) = 16.930664063 Calculate the square root of the right side: 4.114688817 Break this problem into two subproblems by setting (x + 1.34375) equal to 4.114688817 and -4.114688817.Subproblem 1
x + 1.34375 = 4.114688817 Simplifying x + 1.34375 = 4.114688817 Reorder the terms: 1.34375 + x = 4.114688817 Solving 1.34375 + x = 4.114688817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.34375' to each side of the equation. 1.34375 + -1.34375 + x = 4.114688817 + -1.34375 Combine like terms: 1.34375 + -1.34375 = 0.00000 0.00000 + x = 4.114688817 + -1.34375 x = 4.114688817 + -1.34375 Combine like terms: 4.114688817 + -1.34375 = 2.770938817 x = 2.770938817 Simplifying x = 2.770938817Subproblem 2
x + 1.34375 = -4.114688817 Simplifying x + 1.34375 = -4.114688817 Reorder the terms: 1.34375 + x = -4.114688817 Solving 1.34375 + x = -4.114688817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.34375' to each side of the equation. 1.34375 + -1.34375 + x = -4.114688817 + -1.34375 Combine like terms: 1.34375 + -1.34375 = 0.00000 0.00000 + x = -4.114688817 + -1.34375 x = -4.114688817 + -1.34375 Combine like terms: -4.114688817 + -1.34375 = -5.458438817 x = -5.458438817 Simplifying x = -5.458438817Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.770938817, -5.458438817}
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