Simplifying
(x^{4}) + (7x^{2}) + 64 = 0
x^{4} + (7x^{2}) + 64 = 0
Reorder the terms:
64 + (7x^{2}) + x^{4} = 0
Solving
64 + (7x^{2}) + x^{4} = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-64' to each side of the equation.
64 + (7x^{2}) + -64 + x^{4} = 0 + -64
Reorder the terms:
64 + -64 + (7x^{2}) + x^{4} = 0 + -64
Combine like terms: 64 + -64 = 0
0 + (7x^{2}) + x^{4} = 0 + -64
(7x^{2}) + x^{4} = 0 + -64
Combine like terms: 0 + -64 = -64
(7x^{2}) + x^{4} = -64
The x term is (7x^{2}). Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.
Add '12.25' to each side of the equation.
(7x^{2}) + 12.25 + x^{4} = -64 + 12.25
Reorder the terms:
12.25 + (7x^{2}) + x^{4} = -64 + 12.25
Combine like terms: -64 + 12.25 = -51.75
12.25 + (7x^{2}) + x^{4} = -51.75
Factor a perfect square on the left side:
(x^{2} + 3.5)(x^{2} + 3.5) = -51.75
Can't calculate square root of the right side.
The solution to this equation could not be determined.