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Simplifying 0.05x(x + -0.10) = 180 Reorder the terms: 0.05x(-0.10 + x) = 180 (-0.10 * 0.05x + x * 0.05x) = 180 (-0.005x + 0.05x2) = 180 Solving -0.005x + 0.05x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -0.005x + 0.05x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -0.005x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -3600 + -0.1x + x2 = 0 Move the constant term to the right: Add '3600' to each side of the equation. -3600 + -0.1x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + -0.1x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + -0.1x + x2 = 0 + 3600 -0.1x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 -0.1x + x2 = 3600 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 3600 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 3600 + 0.0025 Combine like terms: 3600 + 0.0025 = 3600.0025 0.0025 + -0.1x + x2 = 3600.0025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 3600.0025 Calculate the square root of the right side: 60.000020833 Break this problem into two subproblems by setting (x + -0.05) equal to 60.000020833 and -60.000020833.Subproblem 1
x + -0.05 = 60.000020833 Simplifying x + -0.05 = 60.000020833 Reorder the terms: -0.05 + x = 60.000020833 Solving -0.05 + x = 60.000020833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 60.000020833 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 60.000020833 + 0.05 x = 60.000020833 + 0.05 Combine like terms: 60.000020833 + 0.05 = 60.050020833 x = 60.050020833 Simplifying x = 60.050020833Subproblem 2
x + -0.05 = -60.000020833 Simplifying x + -0.05 = -60.000020833 Reorder the terms: -0.05 + x = -60.000020833 Solving -0.05 + x = -60.000020833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -60.000020833 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -60.000020833 + 0.05 x = -60.000020833 + 0.05 Combine like terms: -60.000020833 + 0.05 = -59.950020833 x = -59.950020833 Simplifying x = -59.950020833Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.050020833, -59.950020833}
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