Solve the following quadratic equation using square roots: (x+3)^2=36 .

Answer 1

To solve the quadratic equation (x+3)^2 = 36 using square roots, we need to isolate x.

Taking the square root of both sides of the equation, we have:
√((x+3)^2) = √36

Simplifying the square root on the left side, we get:
|x+3| = √36

The square root of 36 is 6, so we have:
|x+3| = 6

Now we can solve for x by considering both the positive and negative cases:

1. Positive case:
If |x+3| = 6, then x+3 = 6
Solving for x, we subtract 3 from both sides:
x = 6 - 3
x = 3

2. Negative case:
If |x+3| = 6, then x+3 = -6
Solving for x, we subtract 3 from both sides:
x = -6 - 3
x = -9

So the solutions to the quadratic equation (x+3)^2 = 36 are x = 3 and x = -9.