Final answer:
The equation 4sqrt(x) = x² - 9x + 12 must be re-arranged and then solved using advanced algebraic techniques such as substitution, turning it into a quadratic equation, which can then be factored or solved using the quadratic formula.
Step-by-step explanation:
To solve the equation 4sqrt(x) = x² - 9x + 12, we first need to isolate the square root term by moving all other terms to the opposite side:
x² - 9x + 12 - 4sqrt(x) = 0
This is not a standard quadratic equation because of the square root present; however, it resembles a quadratic in form. We can attempt to factor it, but this unconventional equation may require more advanced techniques such as substitution.
If we tried substitution, let us say y = sqrt(x), then the equation becomes:
y² - 9y + 12 - 4y = 0
Now, it looks like a quadratic equation in terms of y:
y² - 13y + 12 = 0
Which we can factor or use the quadratic formula to solve for y. Once we have the value(s) of y, we can then square it to find the desired x.