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Simplifying x2 + 167x = 6761 Reorder the terms: 167x + x2 = 6761 Solving 167x + x2 = 6761 Solving for variable 'x'. Reorder the terms: -6761 + 167x + x2 = 6761 + -6761 Combine like terms: 6761 + -6761 = 0 -6761 + 167x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6761' to each side of the equation. -6761 + 167x + 6761 + x2 = 0 + 6761 Reorder the terms: -6761 + 6761 + 167x + x2 = 0 + 6761 Combine like terms: -6761 + 6761 = 0 0 + 167x + x2 = 0 + 6761 167x + x2 = 0 + 6761 Combine like terms: 0 + 6761 = 6761 167x + x2 = 6761 The x term is 167x. Take half its coefficient (83.5). Square it (6972.25) and add it to both sides. Add '6972.25' to each side of the equation. 167x + 6972.25 + x2 = 6761 + 6972.25 Reorder the terms: 6972.25 + 167x + x2 = 6761 + 6972.25 Combine like terms: 6761 + 6972.25 = 13733.25 6972.25 + 167x + x2 = 13733.25 Factor a perfect square on the left side: (x + 83.5)(x + 83.5) = 13733.25 Calculate the square root of the right side: 117.188949991 Break this problem into two subproblems by setting (x + 83.5) equal to 117.188949991 and -117.188949991.Subproblem 1
x + 83.5 = 117.188949991 Simplifying x + 83.5 = 117.188949991 Reorder the terms: 83.5 + x = 117.188949991 Solving 83.5 + x = 117.188949991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-83.5' to each side of the equation. 83.5 + -83.5 + x = 117.188949991 + -83.5 Combine like terms: 83.5 + -83.5 = 0.0 0.0 + x = 117.188949991 + -83.5 x = 117.188949991 + -83.5 Combine like terms: 117.188949991 + -83.5 = 33.688949991 x = 33.688949991 Simplifying x = 33.688949991Subproblem 2
x + 83.5 = -117.188949991 Simplifying x + 83.5 = -117.188949991 Reorder the terms: 83.5 + x = -117.188949991 Solving 83.5 + x = -117.188949991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-83.5' to each side of the equation. 83.5 + -83.5 + x = -117.188949991 + -83.5 Combine like terms: 83.5 + -83.5 = 0.0 0.0 + x = -117.188949991 + -83.5 x = -117.188949991 + -83.5 Combine like terms: -117.188949991 + -83.5 = -200.688949991 x = -200.688949991 Simplifying x = -200.688949991Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.688949991, -200.688949991}
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