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Simplifying x2 + 36x + -12 = 0 Reorder the terms: -12 + 36x + x2 = 0 Solving -12 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 36x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 36x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 36x + x2 = 0 + 12 36x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 36x + x2 = 12 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 = 12 + 324 Reorder the terms: 324 + 36x + x2 = 12 + 324 Combine like terms: 12 + 324 = 336 324 + 36x + x2 = 336 Factor a perfect square on the left side: (x + 18)(x + 18) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + 18) equal to 18.33030278 and -18.33030278.Subproblem 1
x + 18 = 18.33030278 Simplifying x + 18 = 18.33030278 Reorder the terms: 18 + x = 18.33030278 Solving 18 + x = 18.33030278 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 = 18.33030278 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.33030278 + -18 x = 18.33030278 + -18 Combine like terms: 18.33030278 + -18 = 0.33030278 x = 0.33030278 Simplifying x = 0.33030278Subproblem 2
x + 18 = -18.33030278 Simplifying x + 18 = -18.33030278 Reorder the terms: 18 + x = -18.33030278 Solving 18 + x = -18.33030278 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 = -18.33030278 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.33030278 + -18 x = -18.33030278 + -18 Combine like terms: -18.33030278 + -18 = -36.33030278 x = -36.33030278 Simplifying x = -36.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.33030278, -36.33030278}
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