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Simplifying x2 + 38x + -625 = 0 Reorder the terms: -625 + 38x + x2 = 0 Solving -625 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '625' to each side of the equation. -625 + 38x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 38x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 38x + x2 = 0 + 625 38x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 38x + x2 = 625 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = 625 + 361 Reorder the terms: 361 + 38x + x2 = 625 + 361 Combine like terms: 625 + 361 = 986 361 + 38x + x2 = 986 Factor a perfect square on the left side: (x + 19)(x + 19) = 986 Calculate the square root of the right side: 31.400636936 Break this problem into two subproblems by setting (x + 19) equal to 31.400636936 and -31.400636936.Subproblem 1
x + 19 = 31.400636936 Simplifying x + 19 = 31.400636936 Reorder the terms: 19 + x = 31.400636936 Solving 19 + x = 31.400636936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 31.400636936 + -19 Combine like terms: 19 + -19 = 0 0 + x = 31.400636936 + -19 x = 31.400636936 + -19 Combine like terms: 31.400636936 + -19 = 12.400636936 x = 12.400636936 Simplifying x = 12.400636936Subproblem 2
x + 19 = -31.400636936 Simplifying x + 19 = -31.400636936 Reorder the terms: 19 + x = -31.400636936 Solving 19 + x = -31.400636936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -31.400636936 + -19 Combine like terms: 19 + -19 = 0 0 + x = -31.400636936 + -19 x = -31.400636936 + -19 Combine like terms: -31.400636936 + -19 = -50.400636936 x = -50.400636936 Simplifying x = -50.400636936Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.400636936, -50.400636936}
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