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Simplifying -1x2 + -0.000018x + 0.0000045 = 0 Reorder the terms: 0.0000045 + -0.000018x + -1x2 = 0 Solving 0.0000045 + -0.000018x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0000045 + 0.000018x + x2 = 0 Move the constant term to the right: Add '0.0000045' to each side of the equation. -0.0000045 + 0.000018x + 0.0000045 + x2 = 0 + 0.0000045 Reorder the terms: -0.0000045 + 0.0000045 + 0.000018x + x2 = 0 + 0.0000045 Combine like terms: -0.0000045 + 0.0000045 = 0.0000000 0.0000000 + 0.000018x + x2 = 0 + 0.0000045 0.000018x + x2 = 0 + 0.0000045 Combine like terms: 0 + 0.0000045 = 0.0000045 0.000018x + x2 = 0.0000045 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 = 0.0000045 + 0.000000000081 Reorder the terms: 0.000000000081 + 0.000018x + x2 = 0.0000045 + 0.000000000081 Combine like terms: 0.0000045 + 0.000000000081 = 0.000004500081 0.000000000081 + 0.000018x + x2 = 0.000004500081 Factor a perfect square on the left side: (x + 0.000009)(x + 0.000009) = 0.000004500081 Calculate the square root of the right side: 0.002121339 Break this problem into two subproblems by setting (x + 0.000009) equal to 0.002121339 and -0.002121339.Subproblem 1
x + 0.000009 = 0.002121339 Simplifying x + 0.000009 = 0.002121339 Reorder the terms: 0.000009 + x = 0.002121339 Solving 0.000009 + x = 0.002121339 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 = 0.002121339 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = 0.002121339 + -0.000009 x = 0.002121339 + -0.000009 Combine like terms: 0.002121339 + -0.000009 = 0.002112339 x = 0.002112339 Simplifying x = 0.002112339Subproblem 2
x + 0.000009 = -0.002121339 Simplifying x + 0.000009 = -0.002121339 Reorder the terms: 0.000009 + x = -0.002121339 Solving 0.000009 + x = -0.002121339 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 = -0.002121339 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = -0.002121339 + -0.000009 x = -0.002121339 + -0.000009 Combine like terms: -0.002121339 + -0.000009 = -0.002130339 x = -0.002130339 Simplifying x = -0.002130339Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002112339, -0.002130339}
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