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Simplifying x2 + -40x + 181 = 0 Reorder the terms: 181 + -40x + x2 = 0 Solving 181 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-181' to each side of the equation. 181 + -40x + -181 + x2 = 0 + -181 Reorder the terms: 181 + -181 + -40x + x2 = 0 + -181 Combine like terms: 181 + -181 = 0 0 + -40x + x2 = 0 + -181 -40x + x2 = 0 + -181 Combine like terms: 0 + -181 = -181 -40x + x2 = -181 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -181 + 400 Reorder the terms: 400 + -40x + x2 = -181 + 400 Combine like terms: -181 + 400 = 219 400 + -40x + x2 = 219 Factor a perfect square on the left side: (x + -20)(x + -20) = 219 Calculate the square root of the right side: 14.798648587 Break this problem into two subproblems by setting (x + -20) equal to 14.798648587 and -14.798648587.Subproblem 1
x + -20 = 14.798648587 Simplifying x + -20 = 14.798648587 Reorder the terms: -20 + x = 14.798648587 Solving -20 + x = 14.798648587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 14.798648587 + 20 Combine like terms: -20 + 20 = 0 0 + x = 14.798648587 + 20 x = 14.798648587 + 20 Combine like terms: 14.798648587 + 20 = 34.798648587 x = 34.798648587 Simplifying x = 34.798648587Subproblem 2
x + -20 = -14.798648587 Simplifying x + -20 = -14.798648587 Reorder the terms: -20 + x = -14.798648587 Solving -20 + x = -14.798648587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -14.798648587 + 20 Combine like terms: -20 + 20 = 0 0 + x = -14.798648587 + 20 x = -14.798648587 + 20 Combine like terms: -14.798648587 + 20 = 5.201351413 x = 5.201351413 Simplifying x = 5.201351413Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.798648587, 5.201351413}
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