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Simplifying x2 + 40x + 41 = 0 Reorder the terms: 41 + 40x + x2 = 0 Solving 41 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 40x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 40x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 40x + x2 = 0 + -41 40x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 40x + x2 = -41 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 = -41 + 400 Reorder the terms: 400 + 40x + x2 = -41 + 400 Combine like terms: -41 + 400 = 359 400 + 40x + x2 = 359 Factor a perfect square on the left side: (x + 20)(x + 20) = 359 Calculate the square root of the right side: 18.947295321 Break this problem into two subproblems by setting (x + 20) equal to 18.947295321 and -18.947295321.Subproblem 1
x + 20 = 18.947295321 Simplifying x + 20 = 18.947295321 Reorder the terms: 20 + x = 18.947295321 Solving 20 + x = 18.947295321 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 = 18.947295321 + -20 Combine like terms: 20 + -20 = 0 0 + x = 18.947295321 + -20 x = 18.947295321 + -20 Combine like terms: 18.947295321 + -20 = -1.052704679 x = -1.052704679 Simplifying x = -1.052704679Subproblem 2
x + 20 = -18.947295321 Simplifying x + 20 = -18.947295321 Reorder the terms: 20 + x = -18.947295321 Solving 20 + x = -18.947295321 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 = -18.947295321 + -20 Combine like terms: 20 + -20 = 0 0 + x = -18.947295321 + -20 x = -18.947295321 + -20 Combine like terms: -18.947295321 + -20 = -38.947295321 x = -38.947295321 Simplifying x = -38.947295321Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.052704679, -38.947295321}
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