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Simplifying x2 + -0.86x + -0.038 = 0 Reorder the terms: -0.038 + -0.86x + x2 = 0 Solving -0.038 + -0.86x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.038' to each side of the equation. -0.038 + -0.86x + 0.038 + x2 = 0 + 0.038 Reorder the terms: -0.038 + 0.038 + -0.86x + x2 = 0 + 0.038 Combine like terms: -0.038 + 0.038 = 0.000 0.000 + -0.86x + x2 = 0 + 0.038 -0.86x + x2 = 0 + 0.038 Combine like terms: 0 + 0.038 = 0.038 -0.86x + x2 = 0.038 The x term is -0.86x. Take half its coefficient (-0.43). Square it (0.1849) and add it to both sides. Add '0.1849' to each side of the equation. -0.86x + 0.1849 + x2 = 0.038 + 0.1849 Reorder the terms: 0.1849 + -0.86x + x2 = 0.038 + 0.1849 Combine like terms: 0.038 + 0.1849 = 0.2229 0.1849 + -0.86x + x2 = 0.2229 Factor a perfect square on the left side: (x + -0.43)(x + -0.43) = 0.2229 Calculate the square root of the right side: 0.472122865 Break this problem into two subproblems by setting (x + -0.43) equal to 0.472122865 and -0.472122865.Subproblem 1
x + -0.43 = 0.472122865 Simplifying x + -0.43 = 0.472122865 Reorder the terms: -0.43 + x = 0.472122865 Solving -0.43 + x = 0.472122865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.43' to each side of the equation. -0.43 + 0.43 + x = 0.472122865 + 0.43 Combine like terms: -0.43 + 0.43 = 0.00 0.00 + x = 0.472122865 + 0.43 x = 0.472122865 + 0.43 Combine like terms: 0.472122865 + 0.43 = 0.902122865 x = 0.902122865 Simplifying x = 0.902122865Subproblem 2
x + -0.43 = -0.472122865 Simplifying x + -0.43 = -0.472122865 Reorder the terms: -0.43 + x = -0.472122865 Solving -0.43 + x = -0.472122865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.43' to each side of the equation. -0.43 + 0.43 + x = -0.472122865 + 0.43 Combine like terms: -0.43 + 0.43 = 0.00 0.00 + x = -0.472122865 + 0.43 x = -0.472122865 + 0.43 Combine like terms: -0.472122865 + 0.43 = -0.042122865 x = -0.042122865 Simplifying x = -0.042122865Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.902122865, -0.042122865}
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