Let's simplify the equation step by step:
Expand the squared term: (x^2 - 2x + 2)^2 = (x^2 - 2x + 2)(x^2 - 2x + 2)
= x^4 - 2x^3 + 2x^3 - 4x^2 + 4x^2 - 4x + 4x + 4
= x^4 - 4x^3 + 4x^2 + 0x + 4
Now place the expanded term back into the equation:
x^4 - 4x^3 + 4x^2 + 0 - x^2 + 2x - 22 = 0
Combine like terms:
x^4 - 4x^3 + 3x^2 + 2x - 22 = 0
Therefore, the simplified form of the equation (x^2 - 2x + 2)^2 - x^2 + 2x - 22 = 0 is x^4 - 4x^3 + 3x^2 + 2x - 22 = 0.
Let's simplify the equation step by step:
Expand the squared term: (x^2 - 2x + 2)^2 = (x^2 - 2x + 2)(x^2 - 2x + 2)
= x^4 - 2x^3 + 2x^3 - 4x^2 + 4x^2 - 4x + 4x + 4
= x^4 - 4x^3 + 4x^2 + 0x + 4
Now place the expanded term back into the equation:
x^4 - 4x^3 + 4x^2 + 0 - x^2 + 2x - 22 = 0
Combine like terms:
x^4 - 4x^3 + 3x^2 + 2x - 22 = 0
Therefore, the simplified form of the equation (x^2 - 2x + 2)^2 - x^2 + 2x - 22 = 0 is x^4 - 4x^3 + 3x^2 + 2x - 22 = 0.