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Simplifying x2 + 38x + -722 = 0 Reorder the terms: -722 + 38x + x2 = 0 Solving -722 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '722' to each side of the equation. -722 + 38x + 722 + x2 = 0 + 722 Reorder the terms: -722 + 722 + 38x + x2 = 0 + 722 Combine like terms: -722 + 722 = 0 0 + 38x + x2 = 0 + 722 38x + x2 = 0 + 722 Combine like terms: 0 + 722 = 722 38x + x2 = 722 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 = 722 + 361 Reorder the terms: 361 + 38x + x2 = 722 + 361 Combine like terms: 722 + 361 = 1083 361 + 38x + x2 = 1083 Factor a perfect square on the left side: (x + 19)(x + 19) = 1083 Calculate the square root of the right side: 32.908965344 Break this problem into two subproblems by setting (x + 19) equal to 32.908965344 and -32.908965344.Subproblem 1
x + 19 = 32.908965344 Simplifying x + 19 = 32.908965344 Reorder the terms: 19 + x = 32.908965344 Solving 19 + x = 32.908965344 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 = 32.908965344 + -19 Combine like terms: 19 + -19 = 0 0 + x = 32.908965344 + -19 x = 32.908965344 + -19 Combine like terms: 32.908965344 + -19 = 13.908965344 x = 13.908965344 Simplifying x = 13.908965344Subproblem 2
x + 19 = -32.908965344 Simplifying x + 19 = -32.908965344 Reorder the terms: 19 + x = -32.908965344 Solving 19 + x = -32.908965344 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 = -32.908965344 + -19 Combine like terms: 19 + -19 = 0 0 + x = -32.908965344 + -19 x = -32.908965344 + -19 Combine like terms: -32.908965344 + -19 = -51.908965344 x = -51.908965344 Simplifying x = -51.908965344Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.908965344, -51.908965344}
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