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Simplifying x2 + 64x + 320 = 0 Reorder the terms: 320 + 64x + x2 = 0 Solving 320 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-320' to each side of the equation. 320 + 64x + -320 + x2 = 0 + -320 Reorder the terms: 320 + -320 + 64x + x2 = 0 + -320 Combine like terms: 320 + -320 = 0 0 + 64x + x2 = 0 + -320 64x + x2 = 0 + -320 Combine like terms: 0 + -320 = -320 64x + x2 = -320 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 = -320 + 1024 Reorder the terms: 1024 + 64x + x2 = -320 + 1024 Combine like terms: -320 + 1024 = 704 1024 + 64x + x2 = 704 Factor a perfect square on the left side: (x + 32)(x + 32) = 704 Calculate the square root of the right side: 26.532998323 Break this problem into two subproblems by setting (x + 32) equal to 26.532998323 and -26.532998323.Subproblem 1
x + 32 = 26.532998323 Simplifying x + 32 = 26.532998323 Reorder the terms: 32 + x = 26.532998323 Solving 32 + x = 26.532998323 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 = 26.532998323 + -32 Combine like terms: 32 + -32 = 0 0 + x = 26.532998323 + -32 x = 26.532998323 + -32 Combine like terms: 26.532998323 + -32 = -5.467001677 x = -5.467001677 Simplifying x = -5.467001677Subproblem 2
x + 32 = -26.532998323 Simplifying x + 32 = -26.532998323 Reorder the terms: 32 + x = -26.532998323 Solving 32 + x = -26.532998323 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 = -26.532998323 + -32 Combine like terms: 32 + -32 = 0 0 + x = -26.532998323 + -32 x = -26.532998323 + -32 Combine like terms: -26.532998323 + -32 = -58.532998323 x = -58.532998323 Simplifying x = -58.532998323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.467001677, -58.532998323}
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