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Simplifying 200x2 + -1x + -150 = 0 Reorder the terms: -150 + -1x + 200x2 = 0 Solving -150 + -1x + 200x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. -0.75 + -0.005x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.005x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.005x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.005x + x2 = 0 + 0.75 -0.005x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.005x + x2 = 0.75 The x term is -0.005x. Take half its coefficient (-0.0025). Square it (0.00000625) and add it to both sides. Add '0.00000625' to each side of the equation. -0.005x + 0.00000625 + x2 = 0.75 + 0.00000625 Reorder the terms: 0.00000625 + -0.005x + x2 = 0.75 + 0.00000625 Combine like terms: 0.75 + 0.00000625 = 0.75000625 0.00000625 + -0.005x + x2 = 0.75000625 Factor a perfect square on the left side: (x + -0.0025)(x + -0.0025) = 0.75000625 Calculate the square root of the right side: 0.866029012 Break this problem into two subproblems by setting (x + -0.0025) equal to 0.866029012 and -0.866029012.Subproblem 1
x + -0.0025 = 0.866029012 Simplifying x + -0.0025 = 0.866029012 Reorder the terms: -0.0025 + x = 0.866029012 Solving -0.0025 + x = 0.866029012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0025' to each side of the equation. -0.0025 + 0.0025 + x = 0.866029012 + 0.0025 Combine like terms: -0.0025 + 0.0025 = 0.0000 0.0000 + x = 0.866029012 + 0.0025 x = 0.866029012 + 0.0025 Combine like terms: 0.866029012 + 0.0025 = 0.868529012 x = 0.868529012 Simplifying x = 0.868529012Subproblem 2
x + -0.0025 = -0.866029012 Simplifying x + -0.0025 = -0.866029012 Reorder the terms: -0.0025 + x = -0.866029012 Solving -0.0025 + x = -0.866029012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0025' to each side of the equation. -0.0025 + 0.0025 + x = -0.866029012 + 0.0025 Combine like terms: -0.0025 + 0.0025 = 0.0000 0.0000 + x = -0.866029012 + 0.0025 x = -0.866029012 + 0.0025 Combine like terms: -0.866029012 + 0.0025 = -0.863529012 x = -0.863529012 Simplifying x = -0.863529012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.868529012, -0.863529012}
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