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Simplifying x2 = 36x + 3600 Reorder the terms: x2 = 3600 + 36x Solving x2 = 3600 + 36x Solving for variable 'x'. Reorder the terms: -3600 + -36x + x2 = 3600 + 36x + -3600 + -36x Reorder the terms: -3600 + -36x + x2 = 3600 + -3600 + 36x + -36x Combine like terms: 3600 + -3600 = 0 -3600 + -36x + x2 = 0 + 36x + -36x -3600 + -36x + x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -3600 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + -36x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + -36x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + -36x + x2 = 0 + 3600 -36x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 -36x + x2 = 3600 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 = 3600 + 324 Reorder the terms: 324 + -36x + x2 = 3600 + 324 Combine like terms: 3600 + 324 = 3924 324 + -36x + x2 = 3924 Factor a perfect square on the left side: (x + -18)(x + -18) = 3924 Calculate the square root of the right side: 62.641839053 Break this problem into two subproblems by setting (x + -18) equal to 62.641839053 and -62.641839053.Subproblem 1
x + -18 = 62.641839053 Simplifying x + -18 = 62.641839053 Reorder the terms: -18 + x = 62.641839053 Solving -18 + x = 62.641839053 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 = 62.641839053 + 18 Combine like terms: -18 + 18 = 0 0 + x = 62.641839053 + 18 x = 62.641839053 + 18 Combine like terms: 62.641839053 + 18 = 80.641839053 x = 80.641839053 Simplifying x = 80.641839053Subproblem 2
x + -18 = -62.641839053 Simplifying x + -18 = -62.641839053 Reorder the terms: -18 + x = -62.641839053 Solving -18 + x = -62.641839053 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 = -62.641839053 + 18 Combine like terms: -18 + 18 = 0 0 + x = -62.641839053 + 18 x = -62.641839053 + 18 Combine like terms: -62.641839053 + 18 = -44.641839053 x = -44.641839053 Simplifying x = -44.641839053Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.641839053, -44.641839053}
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