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Simplifying -0.004x2 + 0.148x + -0.191 = 0 Reorder the terms: -0.191 + 0.148x + -0.004x2 = 0 Solving -0.191 + 0.148x + -0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. 47.75 + -37x + x2 = 0 Move the constant term to the right: Add '-47.75' to each side of the equation. 47.75 + -37x + -47.75 + x2 = 0 + -47.75 Reorder the terms: 47.75 + -47.75 + -37x + x2 = 0 + -47.75 Combine like terms: 47.75 + -47.75 = 0.00 0.00 + -37x + x2 = 0 + -47.75 -37x + x2 = 0 + -47.75 Combine like terms: 0 + -47.75 = -47.75 -37x + x2 = -47.75 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -47.75 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -47.75 + 342.25 Combine like terms: -47.75 + 342.25 = 294.5 342.25 + -37x + x2 = 294.5 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 294.5 Calculate the square root of the right side: 17.161002302 Break this problem into two subproblems by setting (x + -18.5) equal to 17.161002302 and -17.161002302.Subproblem 1
x + -18.5 = 17.161002302 Simplifying x + -18.5 = 17.161002302 Reorder the terms: -18.5 + x = 17.161002302 Solving -18.5 + x = 17.161002302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 17.161002302 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 17.161002302 + 18.5 x = 17.161002302 + 18.5 Combine like terms: 17.161002302 + 18.5 = 35.661002302 x = 35.661002302 Simplifying x = 35.661002302Subproblem 2
x + -18.5 = -17.161002302 Simplifying x + -18.5 = -17.161002302 Reorder the terms: -18.5 + x = -17.161002302 Solving -18.5 + x = -17.161002302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -17.161002302 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -17.161002302 + 18.5 x = -17.161002302 + 18.5 Combine like terms: -17.161002302 + 18.5 = 1.338997698 x = 1.338997698 Simplifying x = 1.338997698Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.661002302, 1.338997698}
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