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Simplifying x2 + -64x + 578 = 0 Reorder the terms: 578 + -64x + x2 = 0 Solving 578 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-578' to each side of the equation. 578 + -64x + -578 + x2 = 0 + -578 Reorder the terms: 578 + -578 + -64x + x2 = 0 + -578 Combine like terms: 578 + -578 = 0 0 + -64x + x2 = 0 + -578 -64x + x2 = 0 + -578 Combine like terms: 0 + -578 = -578 -64x + x2 = -578 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 = -578 + 1024 Reorder the terms: 1024 + -64x + x2 = -578 + 1024 Combine like terms: -578 + 1024 = 446 1024 + -64x + x2 = 446 Factor a perfect square on the left side: (x + -32)(x + -32) = 446 Calculate the square root of the right side: 21.118712082 Break this problem into two subproblems by setting (x + -32) equal to 21.118712082 and -21.118712082.Subproblem 1
x + -32 = 21.118712082 Simplifying x + -32 = 21.118712082 Reorder the terms: -32 + x = 21.118712082 Solving -32 + x = 21.118712082 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 = 21.118712082 + 32 Combine like terms: -32 + 32 = 0 0 + x = 21.118712082 + 32 x = 21.118712082 + 32 Combine like terms: 21.118712082 + 32 = 53.118712082 x = 53.118712082 Simplifying x = 53.118712082Subproblem 2
x + -32 = -21.118712082 Simplifying x + -32 = -21.118712082 Reorder the terms: -32 + x = -21.118712082 Solving -32 + x = -21.118712082 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 = -21.118712082 + 32 Combine like terms: -32 + 32 = 0 0 + x = -21.118712082 + 32 x = -21.118712082 + 32 Combine like terms: -21.118712082 + 32 = 10.881287918 x = 10.881287918 Simplifying x = 10.881287918Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.118712082, 10.881287918}
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