x4+16x2+256. factorise it
Answers
Answer:
Simplifying
x4 + 16x2 + -256 = 0
Reorder the terms:
-256 + 16x2 + x4 = 0
Solving
-256 + 16x2 + x4 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '256' to each side of the equation.
-256 + 16x2 + 256 + x4 = 0 + 256
Reorder the terms:
-256 + 256 + 16x2 + x4 = 0 + 256
Combine like terms: -256 + 256 = 0
0 + 16x2 + x4 = 0 + 256
16x2 + x4 = 0 + 256
Combine like terms: 0 + 256 = 256
16x2 + x4 = 256
The x term is 16x2. Take half its coefficient (8).
Square it (64) and add it to both sides.
Add '64' to each side of the equation.
16x2 + 64 + x4 = 256 + 64
Reorder the terms:
64 + 16x2 + x4 = 256 + 64
Combine like terms: 256 + 64 = 320
64 + 16x2 + x4 = 320
Factor a perfect square on the left side:
(x2 + 8)(x2 + 8) = 320
Calculate the square root of the right side: 17.88854382
Break this problem into two subproblems by setting
(x2 + 8) equal to 17.88854382 and -17.88854382.
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