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Simplifying x2 + -200 + -506 + 36x = 0 Reorder the terms: -200 + -506 + 36x + x2 = 0 Combine like terms: -200 + -506 = -706 -706 + 36x + x2 = 0 Solving -706 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '706' to each side of the equation. -706 + 36x + 706 + x2 = 0 + 706 Reorder the terms: -706 + 706 + 36x + x2 = 0 + 706 Combine like terms: -706 + 706 = 0 0 + 36x + x2 = 0 + 706 36x + x2 = 0 + 706 Combine like terms: 0 + 706 = 706 36x + x2 = 706 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 = 706 + 324 Reorder the terms: 324 + 36x + x2 = 706 + 324 Combine like terms: 706 + 324 = 1030 324 + 36x + x2 = 1030 Factor a perfect square on the left side: (x + 18)(x + 18) = 1030 Calculate the square root of the right side: 32.093613072 Break this problem into two subproblems by setting (x + 18) equal to 32.093613072 and -32.093613072.Subproblem 1
x + 18 = 32.093613072 Simplifying x + 18 = 32.093613072 Reorder the terms: 18 + x = 32.093613072 Solving 18 + x = 32.093613072 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 = 32.093613072 + -18 Combine like terms: 18 + -18 = 0 0 + x = 32.093613072 + -18 x = 32.093613072 + -18 Combine like terms: 32.093613072 + -18 = 14.093613072 x = 14.093613072 Simplifying x = 14.093613072Subproblem 2
x + 18 = -32.093613072 Simplifying x + 18 = -32.093613072 Reorder the terms: 18 + x = -32.093613072 Solving 18 + x = -32.093613072 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 = -32.093613072 + -18 Combine like terms: 18 + -18 = 0 0 + x = -32.093613072 + -18 x = -32.093613072 + -18 Combine like terms: -32.093613072 + -18 = -50.093613072 x = -50.093613072 Simplifying x = -50.093613072Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.093613072, -50.093613072}
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