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

Question

(
𝑥
+
3
)
2
=
36
.(1 point)
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Answer 1

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

1. Take the square root of both sides:

\[ \sqrt{(x + 3)^2} = \sqrt{36} \]

2. Simplify:

Taking the square root yields two possible cases:

\[ x + 3 = 6 \quad \text{or} \quad x + 3 = -6 \]

3. Solve for \(x\) in each case:

   • For \(x + 3 = 6\):

   \[ x = 6 - 3 = 3 \]

   • For \(x + 3 = -6\):

   \[ x = -6 - 3 = -9 \]

4. Final solutions:

The solutions to the equation \((x + 3)^2 = 36\) are:

\[ {3, -9} \]