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Simplifying x2 + -64x + 168 = 0 Reorder the terms: 168 + -64x + x2 = 0 Solving 168 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-168' to each side of the equation. 168 + -64x + -168 + x2 = 0 + -168 Reorder the terms: 168 + -168 + -64x + x2 = 0 + -168 Combine like terms: 168 + -168 = 0 0 + -64x + x2 = 0 + -168 -64x + x2 = 0 + -168 Combine like terms: 0 + -168 = -168 -64x + x2 = -168 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 = -168 + 1024 Reorder the terms: 1024 + -64x + x2 = -168 + 1024 Combine like terms: -168 + 1024 = 856 1024 + -64x + x2 = 856 Factor a perfect square on the left side: (x + -32)(x + -32) = 856 Calculate the square root of the right side: 29.257477677 Break this problem into two subproblems by setting (x + -32) equal to 29.257477677 and -29.257477677.Subproblem 1
x + -32 = 29.257477677 Simplifying x + -32 = 29.257477677 Reorder the terms: -32 + x = 29.257477677 Solving -32 + x = 29.257477677 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 = 29.257477677 + 32 Combine like terms: -32 + 32 = 0 0 + x = 29.257477677 + 32 x = 29.257477677 + 32 Combine like terms: 29.257477677 + 32 = 61.257477677 x = 61.257477677 Simplifying x = 61.257477677Subproblem 2
x + -32 = -29.257477677 Simplifying x + -32 = -29.257477677 Reorder the terms: -32 + x = -29.257477677 Solving -32 + x = -29.257477677 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 = -29.257477677 + 32 Combine like terms: -32 + 32 = 0 0 + x = -29.257477677 + 32 x = -29.257477677 + 32 Combine like terms: -29.257477677 + 32 = 2.742522323 x = 2.742522323 Simplifying x = 2.742522323Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.257477677, 2.742522323}
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