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Simplifying 3.95x2 + 0.05x + -0.008 = 0 Reorder the terms: -0.008 + 0.05x + 3.95x2 = 0 Solving -0.008 + 0.05x + 3.95x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.95 the coefficient of the squared term: Divide each side by '3.95'. -0.002025316456 + 0.01265822785x + x2 = 0 Move the constant term to the right: Add '0.002025316456' to each side of the equation. -0.002025316456 + 0.01265822785x + 0.002025316456 + x2 = 0 + 0.002025316456 Reorder the terms: -0.002025316456 + 0.002025316456 + 0.01265822785x + x2 = 0 + 0.002025316456 Combine like terms: -0.002025316456 + 0.002025316456 = 0.000000000000 0.000000000000 + 0.01265822785x + x2 = 0 + 0.002025316456 0.01265822785x + x2 = 0 + 0.002025316456 Combine like terms: 0 + 0.002025316456 = 0.002025316456 0.01265822785x + x2 = 0.002025316456 The x term is 0.01265822785x. Take half its coefficient (0.006329113925). Square it (0.00004005768308) and add it to both sides. Add '0.00004005768308' to each side of the equation. 0.01265822785x + 0.00004005768308 + x2 = 0.002025316456 + 0.00004005768308 Reorder the terms: 0.00004005768308 + 0.01265822785x + x2 = 0.002025316456 + 0.00004005768308 Combine like terms: 0.002025316456 + 0.00004005768308 = 0.00206537413908 0.00004005768308 + 0.01265822785x + x2 = 0.00206537413908 Factor a perfect square on the left side: (x + 0.006329113925)(x + 0.006329113925) = 0.00206537413908 Calculate the square root of the right side: 0.045446388 Break this problem into two subproblems by setting (x + 0.006329113925) equal to 0.045446388 and -0.045446388.Subproblem 1
x + 0.006329113925 = 0.045446388 Simplifying x + 0.006329113925 = 0.045446388 Reorder the terms: 0.006329113925 + x = 0.045446388 Solving 0.006329113925 + x = 0.045446388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006329113925' to each side of the equation. 0.006329113925 + -0.006329113925 + x = 0.045446388 + -0.006329113925 Combine like terms: 0.006329113925 + -0.006329113925 = 0.000000000000 0.000000000000 + x = 0.045446388 + -0.006329113925 x = 0.045446388 + -0.006329113925 Combine like terms: 0.045446388 + -0.006329113925 = 0.039117274075 x = 0.039117274075 Simplifying x = 0.039117274075Subproblem 2
x + 0.006329113925 = -0.045446388 Simplifying x + 0.006329113925 = -0.045446388 Reorder the terms: 0.006329113925 + x = -0.045446388 Solving 0.006329113925 + x = -0.045446388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006329113925' to each side of the equation. 0.006329113925 + -0.006329113925 + x = -0.045446388 + -0.006329113925 Combine like terms: 0.006329113925 + -0.006329113925 = 0.000000000000 0.000000000000 + x = -0.045446388 + -0.006329113925 x = -0.045446388 + -0.006329113925 Combine like terms: -0.045446388 + -0.006329113925 = -0.051775501925 x = -0.051775501925 Simplifying x = -0.051775501925Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039117274075, -0.051775501925}
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