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Simplifying 100x2 + -181x + 8.1 = 0 Reorder the terms: 8.1 + -181x + 100x2 = 0 Solving 8.1 + -181x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 0.081 + -1.81x + x2 = 0 Move the constant term to the right: Add '-0.081' to each side of the equation. 0.081 + -1.81x + -0.081 + x2 = 0 + -0.081 Reorder the terms: 0.081 + -0.081 + -1.81x + x2 = 0 + -0.081 Combine like terms: 0.081 + -0.081 = 0.000 0.000 + -1.81x + x2 = 0 + -0.081 -1.81x + x2 = 0 + -0.081 Combine like terms: 0 + -0.081 = -0.081 -1.81x + x2 = -0.081 The x term is -1.81x. Take half its coefficient (-0.905). Square it (0.819025) and add it to both sides. Add '0.819025' to each side of the equation. -1.81x + 0.819025 + x2 = -0.081 + 0.819025 Reorder the terms: 0.819025 + -1.81x + x2 = -0.081 + 0.819025 Combine like terms: -0.081 + 0.819025 = 0.738025 0.819025 + -1.81x + x2 = 0.738025 Factor a perfect square on the left side: (x + -0.905)(x + -0.905) = 0.738025 Calculate the square root of the right side: 0.859083814 Break this problem into two subproblems by setting (x + -0.905) equal to 0.859083814 and -0.859083814.Subproblem 1
x + -0.905 = 0.859083814 Simplifying x + -0.905 = 0.859083814 Reorder the terms: -0.905 + x = 0.859083814 Solving -0.905 + x = 0.859083814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.905' to each side of the equation. -0.905 + 0.905 + x = 0.859083814 + 0.905 Combine like terms: -0.905 + 0.905 = 0.000 0.000 + x = 0.859083814 + 0.905 x = 0.859083814 + 0.905 Combine like terms: 0.859083814 + 0.905 = 1.764083814 x = 1.764083814 Simplifying x = 1.764083814Subproblem 2
x + -0.905 = -0.859083814 Simplifying x + -0.905 = -0.859083814 Reorder the terms: -0.905 + x = -0.859083814 Solving -0.905 + x = -0.859083814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.905' to each side of the equation. -0.905 + 0.905 + x = -0.859083814 + 0.905 Combine like terms: -0.905 + 0.905 = 0.000 0.000 + x = -0.859083814 + 0.905 x = -0.859083814 + 0.905 Combine like terms: -0.859083814 + 0.905 = 0.045916186 x = 0.045916186 Simplifying x = 0.045916186Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.764083814, 0.045916186}
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