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Simplifying x4 + 32x2 + -192 = 0 Reorder the terms: -192 + 32x2 + x4 = 0 Solving -192 + 32x2 + x4 = 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 + 32x2 + 192 + x4 = 0 + 192 Reorder the terms: -192 + 192 + 32x2 + x4 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 32x2 + x4 = 0 + 192 32x2 + x4 = 0 + 192 Combine like terms: 0 + 192 = 192 32x2 + x4 = 192 The x term is 32x2. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x2 + 256 + x4 = 192 + 256 Reorder the terms: 256 + 32x2 + x4 = 192 + 256 Combine like terms: 192 + 256 = 448 256 + 32x2 + x4 = 448 Factor a perfect square on the left side: (x2 + 16)(x2 + 16) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x2 + 16) equal to 21.166010489 and -21.166010489.Subproblem 1
x2 + 16 = 21.166010489 Simplifying x2 + 16 = 21.166010489 Reorder the terms: 16 + x2 = 21.166010489 Solving 16 + x2 = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = 21.166010489 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = 21.166010489 + -16 x2 = 21.166010489 + -16 Combine like terms: 21.166010489 + -16 = 5.166010489 x2 = 5.166010489 Simplifying x2 = 5.166010489 Take the square root of each side: x = {-2.272885938, 2.272885938}Subproblem 2
x2 + 16 = -21.166010489 Simplifying x2 + 16 = -21.166010489 Reorder the terms: 16 + x2 = -21.166010489 Solving 16 + x2 = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = -21.166010489 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = -21.166010489 + -16 x2 = -21.166010489 + -16 Combine like terms: -21.166010489 + -16 = -37.166010489 x2 = -37.166010489 Simplifying x2 = -37.166010489 Reorder the terms: 37.166010489 + x2 = -37.166010489 + 37.166010489 Combine like terms: -37.166010489 + 37.166010489 = 0.000000000 37.166010489 + 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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