Question

What are the solutions to the quadratic equation 4(x + 2)2 = 36

Answer 1

4x + 8 x 2 = 36
4x + 16 = 36
4x = 20 
x = 5

Answer 2

Answer:

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

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:

$x+2-2=-2\pm 3$

$x=-2\pm 3$

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

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

$x=-5\text{ or }x=1$

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