Question

factorize 8x^6+5a^3+1

Answer 1

Simplifying
8a6 + 5a3 + 1 = 0

Reorder the terms:
1 + 5a3 + 8a6 = 0

Solving
1 + 5a3 + 8a6 = 0

Solving for variable 'a'.

Begin completing the square. Divide all terms by
8 the coefficient of the squared term:

Divide each side by '8'.
0.125 + 0.625a3 + a6 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 0.625a3 + -0.125 + a6 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 0.625a3 + a6 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 0.625a3 + a6 = 0 + -0.125
0.625a3 + a6 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
0.625a3 + a6 = -0.125

The a term is 0.625a3. Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625a3 + 0.09765625 + a6 = -0.125 + 0.09765625

Reorder the terms:
0.09765625 + 0.625a3 + a6 = -0.125 + 0.09765625

Combine like terms: -0.125 + 0.09765625 = -0.02734375
0.09765625 + 0.625a3 + a6 = -0.02734375

Factor a perfect square on the left side:
(a3 + 0.3125)(a3 + 0.3125) = -0.02734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.