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Simplifying 2x2 + 0.02x + -120 = 0 Reorder the terms: -120 + 0.02x + 2x2 = 0 Solving -120 + 0.02x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + 0.01x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 0.01x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 0.01x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 0.01x + x2 = 0 + 60 0.01x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 0.01x + x2 = 60 The x term is 0.01x. Take half its coefficient (0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. 0.01x + 0.000025 + x2 = 60 + 0.000025 Reorder the terms: 0.000025 + 0.01x + x2 = 60 + 0.000025 Combine like terms: 60 + 0.000025 = 60.000025 0.000025 + 0.01x + x2 = 60.000025 Factor a perfect square on the left side: (x + 0.005)(x + 0.005) = 60.000025 Calculate the square root of the right side: 7.745968306 Break this problem into two subproblems by setting (x + 0.005) equal to 7.745968306 and -7.745968306.Subproblem 1
x + 0.005 = 7.745968306 Simplifying x + 0.005 = 7.745968306 Reorder the terms: 0.005 + x = 7.745968306 Solving 0.005 + x = 7.745968306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = 7.745968306 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = 7.745968306 + -0.005 x = 7.745968306 + -0.005 Combine like terms: 7.745968306 + -0.005 = 7.740968306 x = 7.740968306 Simplifying x = 7.740968306Subproblem 2
x + 0.005 = -7.745968306 Simplifying x + 0.005 = -7.745968306 Reorder the terms: 0.005 + x = -7.745968306 Solving 0.005 + x = -7.745968306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = -7.745968306 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = -7.745968306 + -0.005 x = -7.745968306 + -0.005 Combine like terms: -7.745968306 + -0.005 = -7.750968306 x = -7.750968306 Simplifying x = -7.750968306Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.740968306, -7.750968306}
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