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Simplifying x2 + 36x + -180 = 0 Reorder the terms: -180 + 36x + x2 = 0 Solving -180 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 36x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 36x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 36x + x2 = 0 + 180 36x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 36x + x2 = 180 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 = 180 + 324 Reorder the terms: 324 + 36x + x2 = 180 + 324 Combine like terms: 180 + 324 = 504 324 + 36x + x2 = 504 Factor a perfect square on the left side: (x + 18)(x + 18) = 504 Calculate the square root of the right side: 22.449944321 Break this problem into two subproblems by setting (x + 18) equal to 22.449944321 and -22.449944321.Subproblem 1
x + 18 = 22.449944321 Simplifying x + 18 = 22.449944321 Reorder the terms: 18 + x = 22.449944321 Solving 18 + x = 22.449944321 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 = 22.449944321 + -18 Combine like terms: 18 + -18 = 0 0 + x = 22.449944321 + -18 x = 22.449944321 + -18 Combine like terms: 22.449944321 + -18 = 4.449944321 x = 4.449944321 Simplifying x = 4.449944321Subproblem 2
x + 18 = -22.449944321 Simplifying x + 18 = -22.449944321 Reorder the terms: 18 + x = -22.449944321 Solving 18 + x = -22.449944321 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 = -22.449944321 + -18 Combine like terms: 18 + -18 = 0 0 + x = -22.449944321 + -18 x = -22.449944321 + -18 Combine like terms: -22.449944321 + -18 = -40.449944321 x = -40.449944321 Simplifying x = -40.449944321Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.449944321, -40.449944321}
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