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Simplifying x2 + 64x + -880 = 0 Reorder the terms: -880 + 64x + x2 = 0 Solving -880 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '880' to each side of the equation. -880 + 64x + 880 + x2 = 0 + 880 Reorder the terms: -880 + 880 + 64x + x2 = 0 + 880 Combine like terms: -880 + 880 = 0 0 + 64x + x2 = 0 + 880 64x + x2 = 0 + 880 Combine like terms: 0 + 880 = 880 64x + x2 = 880 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 = 880 + 1024 Reorder the terms: 1024 + 64x + x2 = 880 + 1024 Combine like terms: 880 + 1024 = 1904 1024 + 64x + x2 = 1904 Factor a perfect square on the left side: (x + 32)(x + 32) = 1904 Calculate the square root of the right side: 43.634848459 Break this problem into two subproblems by setting (x + 32) equal to 43.634848459 and -43.634848459.Subproblem 1
x + 32 = 43.634848459 Simplifying x + 32 = 43.634848459 Reorder the terms: 32 + x = 43.634848459 Solving 32 + x = 43.634848459 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 = 43.634848459 + -32 Combine like terms: 32 + -32 = 0 0 + x = 43.634848459 + -32 x = 43.634848459 + -32 Combine like terms: 43.634848459 + -32 = 11.634848459 x = 11.634848459 Simplifying x = 11.634848459Subproblem 2
x + 32 = -43.634848459 Simplifying x + 32 = -43.634848459 Reorder the terms: 32 + x = -43.634848459 Solving 32 + x = -43.634848459 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 = -43.634848459 + -32 Combine like terms: 32 + -32 = 0 0 + x = -43.634848459 + -32 x = -43.634848459 + -32 Combine like terms: -43.634848459 + -32 = -75.634848459 x = -75.634848459 Simplifying x = -75.634848459Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.634848459, -75.634848459}
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