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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 = 180 324 + 36x + x2 = 180 Factor a perfect square on the left side: (x + 18)(x + 18) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 18) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 18 = 13.416407865 Simplifying x + 18 = 13.416407865 Reorder the terms: 18 + x = 13.416407865 Solving 18 + x = 13.416407865 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 = 13.416407865 + -18 Combine like terms: 18 + -18 = 0 0 + x = 13.416407865 + -18 x = 13.416407865 + -18 Combine like terms: 13.416407865 + -18 = -4.583592135 x = -4.583592135 Simplifying x = -4.583592135Subproblem 2
x + 18 = -13.416407865 Simplifying x + 18 = -13.416407865 Reorder the terms: 18 + x = -13.416407865 Solving 18 + x = -13.416407865 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 = -13.416407865 + -18 Combine like terms: 18 + -18 = 0 0 + x = -13.416407865 + -18 x = -13.416407865 + -18 Combine like terms: -13.416407865 + -18 = -31.416407865 x = -31.416407865 Simplifying x = -31.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.583592135, -31.416407865}
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