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Simplifying 10000x2 + -1801x + 81 = 0 Reorder the terms: 81 + -1801x + 10000x2 = 0 Solving 81 + -1801x + 10000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10000 the coefficient of the squared term: Divide each side by '10000'. 0.0081 + -0.1801x + x2 = 0 Move the constant term to the right: Add '-0.0081' to each side of the equation. 0.0081 + -0.1801x + -0.0081 + x2 = 0 + -0.0081 Reorder the terms: 0.0081 + -0.0081 + -0.1801x + x2 = 0 + -0.0081 Combine like terms: 0.0081 + -0.0081 = 0.0000 0.0000 + -0.1801x + x2 = 0 + -0.0081 -0.1801x + x2 = 0 + -0.0081 Combine like terms: 0 + -0.0081 = -0.0081 -0.1801x + x2 = -0.0081 The x term is -0.1801x. Take half its coefficient (-0.09005). Square it (0.0081090025) and add it to both sides. Add '0.0081090025' to each side of the equation. -0.1801x + 0.0081090025 + x2 = -0.0081 + 0.0081090025 Reorder the terms: 0.0081090025 + -0.1801x + x2 = -0.0081 + 0.0081090025 Combine like terms: -0.0081 + 0.0081090025 = 0.0000090025 0.0081090025 + -0.1801x + x2 = 0.0000090025 Factor a perfect square on the left side: (x + -0.09005)(x + -0.09005) = 0.0000090025 Calculate the square root of the right side: 0.003000417 Break this problem into two subproblems by setting (x + -0.09005) equal to 0.003000417 and -0.003000417.Subproblem 1
x + -0.09005 = 0.003000417 Simplifying x + -0.09005 = 0.003000417 Reorder the terms: -0.09005 + x = 0.003000417 Solving -0.09005 + x = 0.003000417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09005' to each side of the equation. -0.09005 + 0.09005 + x = 0.003000417 + 0.09005 Combine like terms: -0.09005 + 0.09005 = 0.00000 0.00000 + x = 0.003000417 + 0.09005 x = 0.003000417 + 0.09005 Combine like terms: 0.003000417 + 0.09005 = 0.093050417 x = 0.093050417 Simplifying x = 0.093050417Subproblem 2
x + -0.09005 = -0.003000417 Simplifying x + -0.09005 = -0.003000417 Reorder the terms: -0.09005 + x = -0.003000417 Solving -0.09005 + x = -0.003000417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09005' to each side of the equation. -0.09005 + 0.09005 + x = -0.003000417 + 0.09005 Combine like terms: -0.09005 + 0.09005 = 0.00000 0.00000 + x = -0.003000417 + 0.09005 x = -0.003000417 + 0.09005 Combine like terms: -0.003000417 + 0.09005 = 0.087049583 x = 0.087049583 Simplifying x = 0.087049583Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.093050417, 0.087049583}
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