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Simplifying 1000x2 + -181x + 8.1 = 0 Reorder the terms: 8.1 + -181x + 1000x2 = 0 Solving 8.1 + -181x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. 0.0081 + -0.181x + x2 = 0 Move the constant term to the right: Add '-0.0081' to each side of the equation. 0.0081 + -0.181x + -0.0081 + x2 = 0 + -0.0081 Reorder the terms: 0.0081 + -0.0081 + -0.181x + x2 = 0 + -0.0081 Combine like terms: 0.0081 + -0.0081 = 0.0000 0.0000 + -0.181x + x2 = 0 + -0.0081 -0.181x + x2 = 0 + -0.0081 Combine like terms: 0 + -0.0081 = -0.0081 -0.181x + x2 = -0.0081 The x term is -0.181x. Take half its coefficient (-0.0905). Square it (0.00819025) and add it to both sides. Add '0.00819025' to each side of the equation. -0.181x + 0.00819025 + x2 = -0.0081 + 0.00819025 Reorder the terms: 0.00819025 + -0.181x + x2 = -0.0081 + 0.00819025 Combine like terms: -0.0081 + 0.00819025 = 0.00009025 0.00819025 + -0.181x + x2 = 0.00009025 Factor a perfect square on the left side: (x + -0.0905)(x + -0.0905) = 0.00009025 Calculate the square root of the right side: 0.0095 Break this problem into two subproblems by setting (x + -0.0905) equal to 0.0095 and -0.0095.Subproblem 1
x + -0.0905 = 0.0095 Simplifying x + -0.0905 = 0.0095 Reorder the terms: -0.0905 + x = 0.0095 Solving -0.0905 + x = 0.0095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0905' to each side of the equation. -0.0905 + 0.0905 + x = 0.0095 + 0.0905 Combine like terms: -0.0905 + 0.0905 = 0.0000 0.0000 + x = 0.0095 + 0.0905 x = 0.0095 + 0.0905 Combine like terms: 0.0095 + 0.0905 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + -0.0905 = -0.0095 Simplifying x + -0.0905 = -0.0095 Reorder the terms: -0.0905 + x = -0.0095 Solving -0.0905 + x = -0.0095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0905' to each side of the equation. -0.0905 + 0.0905 + x = -0.0095 + 0.0905 Combine like terms: -0.0905 + 0.0905 = 0.0000 0.0000 + x = -0.0095 + 0.0905 x = -0.0095 + 0.0905 Combine like terms: -0.0095 + 0.0905 = 0.081 x = 0.081 Simplifying x = 0.081Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, 0.081}
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