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Simplifying x4 + -2x2 + -243 = 0 Reorder the terms: -243 + -2x2 + x4 = 0 Solving -243 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '243' to each side of the equation. -243 + -2x2 + 243 + x4 = 0 + 243 Reorder the terms: -243 + 243 + -2x2 + x4 = 0 + 243 Combine like terms: -243 + 243 = 0 0 + -2x2 + x4 = 0 + 243 -2x2 + x4 = 0 + 243 Combine like terms: 0 + 243 = 243 -2x2 + x4 = 243 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 243 + 1 Reorder the terms: 1 + -2x2 + x4 = 243 + 1 Combine like terms: 243 + 1 = 244 1 + -2x2 + x4 = 244 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x2 + -1) equal to 15.620499352 and -15.620499352.Subproblem 1
x2 + -1 = 15.620499352 Simplifying x2 + -1 = 15.620499352 Reorder the terms: -1 + x2 = 15.620499352 Solving -1 + x2 = 15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 15.620499352 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 15.620499352 + 1 x2 = 15.620499352 + 1 Combine like terms: 15.620499352 + 1 = 16.620499352 x2 = 16.620499352 Simplifying x2 = 16.620499352 Take the square root of each side: x = {-4.076824665, 4.076824665}Subproblem 2
x2 + -1 = -15.620499352 Simplifying x2 + -1 = -15.620499352 Reorder the terms: -1 + x2 = -15.620499352 Solving -1 + x2 = -15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -15.620499352 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -15.620499352 + 1 x2 = -15.620499352 + 1 Combine like terms: -15.620499352 + 1 = -14.620499352 x2 = -14.620499352 Simplifying x2 = -14.620499352 Reorder the terms: 14.620499352 + x2 = -14.620499352 + 14.620499352 Combine like terms: -14.620499352 + 14.620499352 = 0.000000000 14.620499352 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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