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Simplifying 0.100x2 + -2.012x + 0.00035 = 0 Reorder the terms: 0.00035 + -2.012x + 0.100x2 = 0 Solving 0.00035 + -2.012x + 0.100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.100 the coefficient of the squared term: Divide each side by '0.100'. 0.0035 + -20.12x + x2 = 0 Move the constant term to the right: Add '-0.0035' to each side of the equation. 0.0035 + -20.12x + -0.0035 + x2 = 0 + -0.0035 Reorder the terms: 0.0035 + -0.0035 + -20.12x + x2 = 0 + -0.0035 Combine like terms: 0.0035 + -0.0035 = 0.0000 0.0000 + -20.12x + x2 = 0 + -0.0035 -20.12x + x2 = 0 + -0.0035 Combine like terms: 0 + -0.0035 = -0.0035 -20.12x + x2 = -0.0035 The x term is -20.12x. Take half its coefficient (-10.06). Square it (101.2036) and add it to both sides. Add '101.2036' to each side of the equation. -20.12x + 101.2036 + x2 = -0.0035 + 101.2036 Reorder the terms: 101.2036 + -20.12x + x2 = -0.0035 + 101.2036 Combine like terms: -0.0035 + 101.2036 = 101.2001 101.2036 + -20.12x + x2 = 101.2001 Factor a perfect square on the left side: (x + -10.06)(x + -10.06) = 101.2001 Calculate the square root of the right side: 10.059826042 Break this problem into two subproblems by setting (x + -10.06) equal to 10.059826042 and -10.059826042.Subproblem 1
x + -10.06 = 10.059826042 Simplifying x + -10.06 = 10.059826042 Reorder the terms: -10.06 + x = 10.059826042 Solving -10.06 + x = 10.059826042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.06' to each side of the equation. -10.06 + 10.06 + x = 10.059826042 + 10.06 Combine like terms: -10.06 + 10.06 = 0.00 0.00 + x = 10.059826042 + 10.06 x = 10.059826042 + 10.06 Combine like terms: 10.059826042 + 10.06 = 20.119826042 x = 20.119826042 Simplifying x = 20.119826042Subproblem 2
x + -10.06 = -10.059826042 Simplifying x + -10.06 = -10.059826042 Reorder the terms: -10.06 + x = -10.059826042 Solving -10.06 + x = -10.059826042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.06' to each side of the equation. -10.06 + 10.06 + x = -10.059826042 + 10.06 Combine like terms: -10.06 + 10.06 = 0.00 0.00 + x = -10.059826042 + 10.06 x = -10.059826042 + 10.06 Combine like terms: -10.059826042 + 10.06 = 0.000173958 x = 0.000173958 Simplifying x = 0.000173958Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.119826042, 0.000173958}
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