First, let's expand the left side of the equation:
(x^2 + x)^2 = (x^2 + x)(x^2 + x= x^4 + x^3 + x^3 + x^= x^4 + 2x^3 + x^2
Now, let's distribute the -11 to the terms inside the parentheses:
11(x^2 + x) = 11x^2 + 11x
Substitute these back into the equation:
(x^2 + x)^2 - 11(x^2 + x) = x^4 + 2x^3 + x^2 - 11x^2 - 11x
Now, simplify and combine like terms:
x^4 + 2x^3 + x^2 - 11x^2 - 11x = x^4 + 2x^3 - 10x^2 - 11x
We want this to equal 12, so our equation becomes:
x^4 + 2x^3 - 10x^2 - 11x = 12
This is the final equation.
First, let's expand the left side of the equation:
(x^2 + x)^2 = (x^2 + x)(x^2 + x
= x^4 + x^3 + x^3 + x^
= x^4 + 2x^3 + x^2
Now, let's distribute the -11 to the terms inside the parentheses:
11(x^2 + x) = 11x^2 + 11x
Substitute these back into the equation:
(x^2 + x)^2 - 11(x^2 + x) = x^4 + 2x^3 + x^2 - 11x^2 - 11x
Now, simplify and combine like terms:
x^4 + 2x^3 + x^2 - 11x^2 - 11x = x^4 + 2x^3 - 10x^2 - 11x
We want this to equal 12, so our equation becomes:
x^4 + 2x^3 - 10x^2 - 11x = 12
This is the final equation.