x^6-20x^3+343=0

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Solution for x^6-20x^3+343=0 equation:


Simplifying
x6 + -20x3 + 343 = 0

Reorder the terms:
343 + -20x3 + x6 = 0

Solving
343 + -20x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-343' to each side of the equation.
343 + -20x3 + -343 + x6 = 0 + -343

Reorder the terms:
343 + -343 + -20x3 + x6 = 0 + -343

Combine like terms: 343 + -343 = 0
0 + -20x3 + x6 = 0 + -343
-20x3 + x6 = 0 + -343

Combine like terms: 0 + -343 = -343
-20x3 + x6 = -343

The x term is -20x3.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x3 + 100 + x6 = -343 + 100

Reorder the terms:
100 + -20x3 + x6 = -343 + 100

Combine like terms: -343 + 100 = -243
100 + -20x3 + x6 = -243

Factor a perfect square on the left side:
(x3 + -10)(x3 + -10) = -243

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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