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Simplifying x2 + 36x + 29 = 0 Reorder the terms: 29 + 36x + x2 = 0 Solving 29 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 36x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 36x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 36x + x2 = 0 + -29 36x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 36x + x2 = -29 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -29 + 324 Reorder the terms: 324 + 36x + x2 = -29 + 324 Combine like terms: -29 + 324 = 295 324 + 36x + x2 = 295 Factor a perfect square on the left side: (x + 18)(x + 18) = 295 Calculate the square root of the right side: 17.175564037 Break this problem into two subproblems by setting (x + 18) equal to 17.175564037 and -17.175564037.Subproblem 1
x + 18 = 17.175564037 Simplifying x + 18 = 17.175564037 Reorder the terms: 18 + x = 17.175564037 Solving 18 + x = 17.175564037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 17.175564037 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.175564037 + -18 x = 17.175564037 + -18 Combine like terms: 17.175564037 + -18 = -0.824435963 x = -0.824435963 Simplifying x = -0.824435963Subproblem 2
x + 18 = -17.175564037 Simplifying x + 18 = -17.175564037 Reorder the terms: 18 + x = -17.175564037 Solving 18 + x = -17.175564037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -17.175564037 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.175564037 + -18 x = -17.175564037 + -18 Combine like terms: -17.175564037 + -18 = -35.175564037 x = -35.175564037 Simplifying x = -35.175564037Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.824435963, -35.175564037}
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