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Simplifying x2 + -64x + -192 = 0 Reorder the terms: -192 + -64x + x2 = 0 Solving -192 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + -64x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -64x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -64x + x2 = 0 + 192 -64x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -64x + x2 = 192 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 = 192 + 1024 Reorder the terms: 1024 + -64x + x2 = 192 + 1024 Combine like terms: 192 + 1024 = 1216 1024 + -64x + x2 = 1216 Factor a perfect square on the left side: (x + -32)(x + -32) = 1216 Calculate the square root of the right side: 34.871191548 Break this problem into two subproblems by setting (x + -32) equal to 34.871191548 and -34.871191548.Subproblem 1
x + -32 = 34.871191548 Simplifying x + -32 = 34.871191548 Reorder the terms: -32 + x = 34.871191548 Solving -32 + x = 34.871191548 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 = 34.871191548 + 32 Combine like terms: -32 + 32 = 0 0 + x = 34.871191548 + 32 x = 34.871191548 + 32 Combine like terms: 34.871191548 + 32 = 66.871191548 x = 66.871191548 Simplifying x = 66.871191548Subproblem 2
x + -32 = -34.871191548 Simplifying x + -32 = -34.871191548 Reorder the terms: -32 + x = -34.871191548 Solving -32 + x = -34.871191548 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 = -34.871191548 + 32 Combine like terms: -32 + 32 = 0 0 + x = -34.871191548 + 32 x = -34.871191548 + 32 Combine like terms: -34.871191548 + 32 = -2.871191548 x = -2.871191548 Simplifying x = -2.871191548Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.871191548, -2.871191548}
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