To solve this equation, first expand the terms inside the parentheses:
(x^2 + x + 3)^2 = x^4 + 2x^3 + 9x^2 + 2x^2 + 6x + = x^4 + 2x^3 + 11x^2 + 6x + 9
Now the equation becomes:
x^4 + 2x^3 + 11x^2 + 6x + 9 + 12x^2 + 12x - 9 = x^4 + 2x^3 + 23x^2 + 18x = 0
Now factor out an x:
x(x^3 + 2x^2 + 23x + 18) = 0
Now we can solve for x by setting each factor to zero:
x = 0
To solve the cubic equation x^3 + 2x^2 + 23x + 18 = 0, we can use numerical methods or factor it into linear and quadratic factors.
To solve this equation, first expand the terms inside the parentheses:
(x^2 + x + 3)^2 = x^4 + 2x^3 + 9x^2 + 2x^2 + 6x +
= x^4 + 2x^3 + 11x^2 + 6x + 9
Now the equation becomes:
x^4 + 2x^3 + 11x^2 + 6x + 9 + 12x^2 + 12x - 9 =
x^4 + 2x^3 + 23x^2 + 18x = 0
Now factor out an x:
x(x^3 + 2x^2 + 23x + 18) = 0
Now we can solve for x by setting each factor to zero:
x = 0
To solve the cubic equation x^3 + 2x^2 + 23x + 18 = 0, we can use numerical methods or factor it into linear and quadratic factors.