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Simplifying x2 + 64x + -1595 = 0 Reorder the terms: -1595 + 64x + x2 = 0 Solving -1595 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1595' to each side of the equation. -1595 + 64x + 1595 + x2 = 0 + 1595 Reorder the terms: -1595 + 1595 + 64x + x2 = 0 + 1595 Combine like terms: -1595 + 1595 = 0 0 + 64x + x2 = 0 + 1595 64x + x2 = 0 + 1595 Combine like terms: 0 + 1595 = 1595 64x + x2 = 1595 The x term is 64x. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x + 1024 + x2 = 1595 + 1024 Reorder the terms: 1024 + 64x + x2 = 1595 + 1024 Combine like terms: 1595 + 1024 = 2619 1024 + 64x + x2 = 2619 Factor a perfect square on the left side: (x + 32)(x + 32) = 2619 Calculate the square root of the right side: 51.176166328 Break this problem into two subproblems by setting (x + 32) equal to 51.176166328 and -51.176166328.Subproblem 1
x + 32 = 51.176166328 Simplifying x + 32 = 51.176166328 Reorder the terms: 32 + x = 51.176166328 Solving 32 + x = 51.176166328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 51.176166328 + -32 Combine like terms: 32 + -32 = 0 0 + x = 51.176166328 + -32 x = 51.176166328 + -32 Combine like terms: 51.176166328 + -32 = 19.176166328 x = 19.176166328 Simplifying x = 19.176166328Subproblem 2
x + 32 = -51.176166328 Simplifying x + 32 = -51.176166328 Reorder the terms: 32 + x = -51.176166328 Solving 32 + x = -51.176166328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -51.176166328 + -32 Combine like terms: 32 + -32 = 0 0 + x = -51.176166328 + -32 x = -51.176166328 + -32 Combine like terms: -51.176166328 + -32 = -83.176166328 x = -83.176166328 Simplifying x = -83.176166328Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.176166328, -83.176166328}
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