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Simplifying -1x2 + -0.00091x + 0.00182 = 0 Reorder the terms: 0.00182 + -0.00091x + -1x2 = 0 Solving 0.00182 + -0.00091x + -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'. -0.00182 + 0.00091x + x2 = 0 Move the constant term to the right: Add '0.00182' to each side of the equation. -0.00182 + 0.00091x + 0.00182 + x2 = 0 + 0.00182 Reorder the terms: -0.00182 + 0.00182 + 0.00091x + x2 = 0 + 0.00182 Combine like terms: -0.00182 + 0.00182 = 0.00000 0.00000 + 0.00091x + x2 = 0 + 0.00182 0.00091x + x2 = 0 + 0.00182 Combine like terms: 0 + 0.00182 = 0.00182 0.00091x + x2 = 0.00182 The x term is 0.00091x. Take half its coefficient (0.000455). Square it (0.000000207025) and add it to both sides. Add '0.000000207025' to each side of the equation. 0.00091x + 0.000000207025 + x2 = 0.00182 + 0.000000207025 Reorder the terms: 0.000000207025 + 0.00091x + x2 = 0.00182 + 0.000000207025 Combine like terms: 0.00182 + 0.000000207025 = 0.001820207025 0.000000207025 + 0.00091x + x2 = 0.001820207025 Factor a perfect square on the left side: (x + 0.000455)(x + 0.000455) = 0.001820207025 Calculate the square root of the right side: 0.042663884 Break this problem into two subproblems by setting (x + 0.000455) equal to 0.042663884 and -0.042663884.Subproblem 1
x + 0.000455 = 0.042663884 Simplifying x + 0.000455 = 0.042663884 Reorder the terms: 0.000455 + x = 0.042663884 Solving 0.000455 + x = 0.042663884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000455' to each side of the equation. 0.000455 + -0.000455 + x = 0.042663884 + -0.000455 Combine like terms: 0.000455 + -0.000455 = 0.000000 0.000000 + x = 0.042663884 + -0.000455 x = 0.042663884 + -0.000455 Combine like terms: 0.042663884 + -0.000455 = 0.042208884 x = 0.042208884 Simplifying x = 0.042208884Subproblem 2
x + 0.000455 = -0.042663884 Simplifying x + 0.000455 = -0.042663884 Reorder the terms: 0.000455 + x = -0.042663884 Solving 0.000455 + x = -0.042663884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000455' to each side of the equation. 0.000455 + -0.000455 + x = -0.042663884 + -0.000455 Combine like terms: 0.000455 + -0.000455 = 0.000000 0.000000 + x = -0.042663884 + -0.000455 x = -0.042663884 + -0.000455 Combine like terms: -0.042663884 + -0.000455 = -0.043118884 x = -0.043118884 Simplifying x = -0.043118884Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.042208884, -0.043118884}
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