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Simplifying (0.000018)(0.2 + -1x) = x2 (0.2 * 0.000018 + -1x * 0.000018) = x2 (0.0000036 + -0.000018x) = x2 Solving 0.0000036 + -0.000018x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.0000036 + -0.000018x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0000036 + 0.000018x + x2 = 0 Move the constant term to the right: Add '0.0000036' to each side of the equation. -0.0000036 + 0.000018x + 0.0000036 + x2 = 0 + 0.0000036 Reorder the terms: -0.0000036 + 0.0000036 + 0.000018x + x2 = 0 + 0.0000036 Combine like terms: -0.0000036 + 0.0000036 = 0.0000000 0.0000000 + 0.000018x + x2 = 0 + 0.0000036 0.000018x + x2 = 0 + 0.0000036 Combine like terms: 0 + 0.0000036 = 0.0000036 0.000018x + x2 = 0.0000036 The x term is 0.000018x. Take half its coefficient (0.000009). Square it (0.000000000081) and add it to both sides. Add '0.000000000081' to each side of the equation. 0.000018x + 0.000000000081 + x2 = 0.0000036 + 0.000000000081 Reorder the terms: 0.000000000081 + 0.000018x + x2 = 0.0000036 + 0.000000000081 Combine like terms: 0.0000036 + 0.000000000081 = 0.000003600081 0.000000000081 + 0.000018x + x2 = 0.000003600081 Factor a perfect square on the left side: (x + 0.000009)(x + 0.000009) = 0.000003600081 Calculate the square root of the right side: 0.001897388 Break this problem into two subproblems by setting (x + 0.000009) equal to 0.001897388 and -0.001897388.Subproblem 1
x + 0.000009 = 0.001897388 Simplifying x + 0.000009 = 0.001897388 Reorder the terms: 0.000009 + x = 0.001897388 Solving 0.000009 + x = 0.001897388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = 0.001897388 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = 0.001897388 + -0.000009 x = 0.001897388 + -0.000009 Combine like terms: 0.001897388 + -0.000009 = 0.001888388 x = 0.001888388 Simplifying x = 0.001888388Subproblem 2
x + 0.000009 = -0.001897388 Simplifying x + 0.000009 = -0.001897388 Reorder the terms: 0.000009 + x = -0.001897388 Solving 0.000009 + x = -0.001897388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = -0.001897388 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = -0.001897388 + -0.000009 x = -0.001897388 + -0.000009 Combine like terms: -0.001897388 + -0.000009 = -0.001906388 x = -0.001906388 Simplifying x = -0.001906388Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001888388, -0.001906388}
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