Answer:

x=-5text{ or }x=1.

Step-by-step explanation:

We have been given a quadratic equation 4(x+2)^2=36. We are asked to find the solutions for our given equation.

First of all, we will divide both sides of our given equation by 4 as shown below:

frac{4(x+2)^2}{4}=frac{36}{4}

(x+2)^2=9

Now, we will take square root of both sides of our equation.

sqrt{(x+2)^2}=pm sqrt{9}

sqrt{(x+2)^2}=pm sqrt{3^2}

Using radical rule sqrt[n]{a^n}=a, we will get:

x+2=pm 3

Upon subtracting 2 from both sides of our given equation, we will get:

x+2-2=-2pm 3

x=-2pm 3

Now, we will write two equivalent equations to our equation as:

x=-2-3text{ or }x=-2+3

x=-5text{ or }x=1

Therefore, the solutions for our given quadratic equation are x=-5text{ or }x=1.