How do you solve #4sqrt(x)=-x-3 #?

Since R H S is always negative and L H S is always positive for any positive value of x, there is no actual solution.

A negative value of x makes L H S imaginary.

To solve the equation 4√(x) = -x - 3, we can follow these steps:

1. Start by isolating the square root term on one side of the equation. Add x to both sides to get 4√(x) + x = -3.

2. Square both sides of the equation to eliminate the square root. This gives us (4√(x) + x)^2 = (-3)^2.

3. Simplify the left side of the equation by expanding the square. (4√(x) + x)^2 = (4√(x))^2 + 2(4√(x))(x) + x^2.

4. Simplify further: 16x + 8√(x^3) + x^2 = 9.

5. Rearrange the equation to bring all terms to one side: 8√(x^3) + 16x + x^2 - 9 = 0.

6. At this point, it is difficult to solve the equation algebraically. You can use numerical methods or approximation techniques to find the value of x that satisfies the equation.

Please note that the solution may involve complex numbers or may not have a real solution, depending on the value of x.