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Simplifying x2 + 36x + -100 = 0 Reorder the terms: -100 + 36x + x2 = 0 Solving -100 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 36x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 36x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 36x + x2 = 0 + 100 36x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 36x + x2 = 100 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 = 100 + 324 Reorder the terms: 324 + 36x + x2 = 100 + 324 Combine like terms: 100 + 324 = 424 324 + 36x + x2 = 424 Factor a perfect square on the left side: (x + 18)(x + 18) = 424 Calculate the square root of the right side: 20.591260282 Break this problem into two subproblems by setting (x + 18) equal to 20.591260282 and -20.591260282.Subproblem 1
x + 18 = 20.591260282 Simplifying x + 18 = 20.591260282 Reorder the terms: 18 + x = 20.591260282 Solving 18 + x = 20.591260282 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 = 20.591260282 + -18 Combine like terms: 18 + -18 = 0 0 + x = 20.591260282 + -18 x = 20.591260282 + -18 Combine like terms: 20.591260282 + -18 = 2.591260282 x = 2.591260282 Simplifying x = 2.591260282Subproblem 2
x + 18 = -20.591260282 Simplifying x + 18 = -20.591260282 Reorder the terms: 18 + x = -20.591260282 Solving 18 + x = -20.591260282 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 = -20.591260282 + -18 Combine like terms: 18 + -18 = 0 0 + x = -20.591260282 + -18 x = -20.591260282 + -18 Combine like terms: -20.591260282 + -18 = -38.591260282 x = -38.591260282 Simplifying x = -38.591260282Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.591260282, -38.591260282}
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