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Simplifying x4 + -32x2 + -384 = 0 Reorder the terms: -384 + -32x2 + x4 = 0 Solving -384 + -32x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + -32x2 + 384 + x4 = 0 + 384 Reorder the terms: -384 + 384 + -32x2 + x4 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + -32x2 + x4 = 0 + 384 -32x2 + x4 = 0 + 384 Combine like terms: 0 + 384 = 384 -32x2 + x4 = 384 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 = 384 + 256 Reorder the terms: 256 + -32x2 + x4 = 384 + 256 Combine like terms: 384 + 256 = 640 256 + -32x2 + x4 = 640 Factor a perfect square on the left side: (x2 + -16)(x2 + -16) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (x2 + -16) equal to 25.298221281 and -25.298221281.Subproblem 1
x2 + -16 = 25.298221281 Simplifying x2 + -16 = 25.298221281 Reorder the terms: -16 + x2 = 25.298221281 Solving -16 + x2 = 25.298221281 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 = 25.298221281 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 25.298221281 + 16 x2 = 25.298221281 + 16 Combine like terms: 25.298221281 + 16 = 41.298221281 x2 = 41.298221281 Simplifying x2 = 41.298221281 Take the square root of each side: x = {-6.426369214, 6.426369214}Subproblem 2
x2 + -16 = -25.298221281 Simplifying x2 + -16 = -25.298221281 Reorder the terms: -16 + x2 = -25.298221281 Solving -16 + x2 = -25.298221281 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 = -25.298221281 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -25.298221281 + 16 x2 = -25.298221281 + 16 Combine like terms: -25.298221281 + 16 = -9.298221281 x2 = -9.298221281 Simplifying x2 = -9.298221281 Reorder the terms: 9.298221281 + x2 = -9.298221281 + 9.298221281 Combine like terms: -9.298221281 + 9.298221281 = 0.000000000 9.298221281 + 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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