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Simplifying x2 + 40x + 329 = 0 Reorder the terms: 329 + 40x + x2 = 0 Solving 329 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-329' to each side of the equation. 329 + 40x + -329 + x2 = 0 + -329 Reorder the terms: 329 + -329 + 40x + x2 = 0 + -329 Combine like terms: 329 + -329 = 0 0 + 40x + x2 = 0 + -329 40x + x2 = 0 + -329 Combine like terms: 0 + -329 = -329 40x + x2 = -329 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 = -329 + 400 Reorder the terms: 400 + 40x + x2 = -329 + 400 Combine like terms: -329 + 400 = 71 400 + 40x + x2 = 71 Factor a perfect square on the left side: (x + 20)(x + 20) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 20) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 20 = 8.426149773 Simplifying x + 20 = 8.426149773 Reorder the terms: 20 + x = 8.426149773 Solving 20 + x = 8.426149773 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 = 8.426149773 + -20 Combine like terms: 20 + -20 = 0 0 + x = 8.426149773 + -20 x = 8.426149773 + -20 Combine like terms: 8.426149773 + -20 = -11.573850227 x = -11.573850227 Simplifying x = -11.573850227Subproblem 2
x + 20 = -8.426149773 Simplifying x + 20 = -8.426149773 Reorder the terms: 20 + x = -8.426149773 Solving 20 + x = -8.426149773 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 = -8.426149773 + -20 Combine like terms: 20 + -20 = 0 0 + x = -8.426149773 + -20 x = -8.426149773 + -20 Combine like terms: -8.426149773 + -20 = -28.426149773 x = -28.426149773 Simplifying x = -28.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.573850227, -28.426149773}
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