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Simplifying x2 + 36x + 23 = 0 Reorder the terms: 23 + 36x + x2 = 0 Solving 23 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 36x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 36x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 36x + x2 = 0 + -23 36x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 36x + x2 = -23 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 = -23 + 324 Reorder the terms: 324 + 36x + x2 = -23 + 324 Combine like terms: -23 + 324 = 301 324 + 36x + x2 = 301 Factor a perfect square on the left side: (x + 18)(x + 18) = 301 Calculate the square root of the right side: 17.349351573 Break this problem into two subproblems by setting (x + 18) equal to 17.349351573 and -17.349351573.Subproblem 1
x + 18 = 17.349351573 Simplifying x + 18 = 17.349351573 Reorder the terms: 18 + x = 17.349351573 Solving 18 + x = 17.349351573 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 = 17.349351573 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.349351573 + -18 x = 17.349351573 + -18 Combine like terms: 17.349351573 + -18 = -0.650648427 x = -0.650648427 Simplifying x = -0.650648427Subproblem 2
x + 18 = -17.349351573 Simplifying x + 18 = -17.349351573 Reorder the terms: 18 + x = -17.349351573 Solving 18 + x = -17.349351573 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 = -17.349351573 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.349351573 + -18 x = -17.349351573 + -18 Combine like terms: -17.349351573 + -18 = -35.349351573 x = -35.349351573 Simplifying x = -35.349351573Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.650648427, -35.349351573}
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