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Simplifying x4 + -12x2 + -32 = 0 Reorder the terms: -32 + -12x2 + x4 = 0 Solving -32 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -12x2 + 32 + x4 = 0 + 32 Reorder the terms: -32 + 32 + -12x2 + x4 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -12x2 + x4 = 0 + 32 -12x2 + x4 = 0 + 32 Combine like terms: 0 + 32 = 32 -12x2 + x4 = 32 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = 32 + 36 Reorder the terms: 36 + -12x2 + x4 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + -12x2 + x4 = 68 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x2 + -6) equal to 8.246211251 and -8.246211251.Subproblem 1
x2 + -6 = 8.246211251 Simplifying x2 + -6 = 8.246211251 Reorder the terms: -6 + x2 = 8.246211251 Solving -6 + x2 = 8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 8.246211251 + 6 x2 = 8.246211251 + 6 Combine like terms: 8.246211251 + 6 = 14.246211251 x2 = 14.246211251 Simplifying x2 = 14.246211251 Take the square root of each side: x = {-3.774415352, 3.774415352}Subproblem 2
x2 + -6 = -8.246211251 Simplifying x2 + -6 = -8.246211251 Reorder the terms: -6 + x2 = -8.246211251 Solving -6 + x2 = -8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -8.246211251 + 6 x2 = -8.246211251 + 6 Combine like terms: -8.246211251 + 6 = -2.246211251 x2 = -2.246211251 Simplifying x2 = -2.246211251 Reorder the terms: 2.246211251 + x2 = -2.246211251 + 2.246211251 Combine like terms: -2.246211251 + 2.246211251 = 0.000000000 2.246211251 + 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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