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Simplifying 250 = 0.05x2 + 11x Reorder the terms: 250 = 11x + 0.05x2 Solving 250 = 11x + 0.05x2 Solving for variable 'x'. Reorder the terms: 250 + -11x + -0.05x2 = 11x + -11x + 0.05x2 + -0.05x2 Combine like terms: 11x + -11x = 0 250 + -11x + -0.05x2 = 0 + 0.05x2 + -0.05x2 250 + -11x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 250 + -11x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -5000 + 220x + x2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 220x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 220x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 220x + x2 = 0 + 5000 220x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 220x + x2 = 5000 The x term is 220x. Take half its coefficient (110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. 220x + 12100 + x2 = 5000 + 12100 Reorder the terms: 12100 + 220x + x2 = 5000 + 12100 Combine like terms: 5000 + 12100 = 17100 12100 + 220x + x2 = 17100 Factor a perfect square on the left side: (x + 110)(x + 110) = 17100 Calculate the square root of the right side: 130.766968306 Break this problem into two subproblems by setting (x + 110) equal to 130.766968306 and -130.766968306.Subproblem 1
x + 110 = 130.766968306 Simplifying x + 110 = 130.766968306 Reorder the terms: 110 + x = 130.766968306 Solving 110 + x = 130.766968306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + x = 130.766968306 + -110 Combine like terms: 110 + -110 = 0 0 + x = 130.766968306 + -110 x = 130.766968306 + -110 Combine like terms: 130.766968306 + -110 = 20.766968306 x = 20.766968306 Simplifying x = 20.766968306Subproblem 2
x + 110 = -130.766968306 Simplifying x + 110 = -130.766968306 Reorder the terms: 110 + x = -130.766968306 Solving 110 + x = -130.766968306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + x = -130.766968306 + -110 Combine like terms: 110 + -110 = 0 0 + x = -130.766968306 + -110 x = -130.766968306 + -110 Combine like terms: -130.766968306 + -110 = -240.766968306 x = -240.766968306 Simplifying x = -240.766968306Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.766968306, -240.766968306}
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