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Simplifying x2 + -64x + -1920 = 0 Reorder the terms: -1920 + -64x + x2 = 0 Solving -1920 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1920' to each side of the equation. -1920 + -64x + 1920 + x2 = 0 + 1920 Reorder the terms: -1920 + 1920 + -64x + x2 = 0 + 1920 Combine like terms: -1920 + 1920 = 0 0 + -64x + x2 = 0 + 1920 -64x + x2 = 0 + 1920 Combine like terms: 0 + 1920 = 1920 -64x + x2 = 1920 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 = 1920 + 1024 Reorder the terms: 1024 + -64x + x2 = 1920 + 1024 Combine like terms: 1920 + 1024 = 2944 1024 + -64x + x2 = 2944 Factor a perfect square on the left side: (x + -32)(x + -32) = 2944 Calculate the square root of the right side: 54.258639865 Break this problem into two subproblems by setting (x + -32) equal to 54.258639865 and -54.258639865.Subproblem 1
x + -32 = 54.258639865 Simplifying x + -32 = 54.258639865 Reorder the terms: -32 + x = 54.258639865 Solving -32 + x = 54.258639865 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 = 54.258639865 + 32 Combine like terms: -32 + 32 = 0 0 + x = 54.258639865 + 32 x = 54.258639865 + 32 Combine like terms: 54.258639865 + 32 = 86.258639865 x = 86.258639865 Simplifying x = 86.258639865Subproblem 2
x + -32 = -54.258639865 Simplifying x + -32 = -54.258639865 Reorder the terms: -32 + x = -54.258639865 Solving -32 + x = -54.258639865 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 = -54.258639865 + 32 Combine like terms: -32 + 32 = 0 0 + x = -54.258639865 + 32 x = -54.258639865 + 32 Combine like terms: -54.258639865 + 32 = -22.258639865 x = -22.258639865 Simplifying x = -22.258639865Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.258639865, -22.258639865}
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