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Simplifying x(x + -0.05) = 300 Reorder the terms: x(-0.05 + x) = 300 (-0.05 * x + x * x) = 300 (-0.05x + x2) = 300 Solving -0.05x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + -0.05x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + -0.05x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + -0.05x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -0.05x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -0.05x + x2 = 0 + 300 -0.05x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -0.05x + x2 = 300 The x term is -0.05x. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05x + 0.000625 + x2 = 300 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 300 + 0.000625 Combine like terms: 300 + 0.000625 = 300.000625 0.000625 + -0.05x + x2 = 300.000625 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 300.000625 Calculate the square root of the right side: 17.320526118 Break this problem into two subproblems by setting (x + -0.025) equal to 17.320526118 and -17.320526118.Subproblem 1
x + -0.025 = 17.320526118 Simplifying x + -0.025 = 17.320526118 Reorder the terms: -0.025 + x = 17.320526118 Solving -0.025 + x = 17.320526118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 17.320526118 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 17.320526118 + 0.025 x = 17.320526118 + 0.025 Combine like terms: 17.320526118 + 0.025 = 17.345526118 x = 17.345526118 Simplifying x = 17.345526118Subproblem 2
x + -0.025 = -17.320526118 Simplifying x + -0.025 = -17.320526118 Reorder the terms: -0.025 + x = -17.320526118 Solving -0.025 + x = -17.320526118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -17.320526118 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -17.320526118 + 0.025 x = -17.320526118 + 0.025 Combine like terms: -17.320526118 + 0.025 = -17.295526118 x = -17.295526118 Simplifying x = -17.295526118Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.345526118, -17.295526118}
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