Question

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

Answer 1

use the square roots

Answer 2

(x-6)^2=51

Answer 3

To solve the quadratic equation \((x+3)^2 = 36\) using square roots, we can follow these steps:

1. Take the square root of both sides:
\[
\sqrt{(x+3)^2} = \sqrt{36}
\]
This gives us:
\[
x + 3 = 6 \quad \text{or} \quad x + 3 = -6
\]

2. Solve for \(x\) in both cases:

For the first case:
\[
x + 3 = 6
\]
Subtract 3 from both sides:
\[
x = 6 - 3 = 3
\]

For the second case:
\[
x + 3 = -6
\]
Subtract 3 from both sides:
\[
x = -6 - 3 = -9
\]

3. Therefore, the solutions to the equation \((x+3)^2 = 36\) are:
\[
x = 3 \quad \text{and} \quad x = -9
\]

In conclusion, the solutions are \(x = 3\) and \(x = -9\).