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Simplifying x2 + 36x + -144 = 0 Reorder the terms: -144 + 36x + x2 = 0 Solving -144 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 36x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 36x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 36x + x2 = 0 + 144 36x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 36x + x2 = 144 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 = 144 + 324 Reorder the terms: 324 + 36x + x2 = 144 + 324 Combine like terms: 144 + 324 = 468 324 + 36x + x2 = 468 Factor a perfect square on the left side: (x + 18)(x + 18) = 468 Calculate the square root of the right side: 21.633307653 Break this problem into two subproblems by setting (x + 18) equal to 21.633307653 and -21.633307653.Subproblem 1
x + 18 = 21.633307653 Simplifying x + 18 = 21.633307653 Reorder the terms: 18 + x = 21.633307653 Solving 18 + x = 21.633307653 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 = 21.633307653 + -18 Combine like terms: 18 + -18 = 0 0 + x = 21.633307653 + -18 x = 21.633307653 + -18 Combine like terms: 21.633307653 + -18 = 3.633307653 x = 3.633307653 Simplifying x = 3.633307653Subproblem 2
x + 18 = -21.633307653 Simplifying x + 18 = -21.633307653 Reorder the terms: 18 + x = -21.633307653 Solving 18 + x = -21.633307653 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 = -21.633307653 + -18 Combine like terms: 18 + -18 = 0 0 + x = -21.633307653 + -18 x = -21.633307653 + -18 Combine like terms: -21.633307653 + -18 = -39.633307653 x = -39.633307653 Simplifying x = -39.633307653Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.633307653, -39.633307653}
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