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Simplifying x2 + 64x + -2475 = 0 Reorder the terms: -2475 + 64x + x2 = 0 Solving -2475 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2475' to each side of the equation. -2475 + 64x + 2475 + x2 = 0 + 2475 Reorder the terms: -2475 + 2475 + 64x + x2 = 0 + 2475 Combine like terms: -2475 + 2475 = 0 0 + 64x + x2 = 0 + 2475 64x + x2 = 0 + 2475 Combine like terms: 0 + 2475 = 2475 64x + x2 = 2475 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 = 2475 + 1024 Reorder the terms: 1024 + 64x + x2 = 2475 + 1024 Combine like terms: 2475 + 1024 = 3499 1024 + 64x + x2 = 3499 Factor a perfect square on the left side: (x + 32)(x + 32) = 3499 Calculate the square root of the right side: 59.152345685 Break this problem into two subproblems by setting (x + 32) equal to 59.152345685 and -59.152345685.Subproblem 1
x + 32 = 59.152345685 Simplifying x + 32 = 59.152345685 Reorder the terms: 32 + x = 59.152345685 Solving 32 + x = 59.152345685 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 = 59.152345685 + -32 Combine like terms: 32 + -32 = 0 0 + x = 59.152345685 + -32 x = 59.152345685 + -32 Combine like terms: 59.152345685 + -32 = 27.152345685 x = 27.152345685 Simplifying x = 27.152345685Subproblem 2
x + 32 = -59.152345685 Simplifying x + 32 = -59.152345685 Reorder the terms: 32 + x = -59.152345685 Solving 32 + x = -59.152345685 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 = -59.152345685 + -32 Combine like terms: 32 + -32 = 0 0 + x = -59.152345685 + -32 x = -59.152345685 + -32 Combine like terms: -59.152345685 + -32 = -91.152345685 x = -91.152345685 Simplifying x = -91.152345685Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.152345685, -91.152345685}
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