Question

(x+3)^2 - 81 = 0

Explanation:

Step1: Isolate the squared term

We start with the equation \((x + 3)^2-81 = 0\). First, we add 81 to both sides of the equation to isolate the squared term.

$$ (x + 3)^2=81 $$

Step2: Take square roots

Next, we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative root. So we have:

$$ x + 3=\pm\sqrt{81} $$

Since \(\sqrt{81} = 9\), this simplifies to:

$$ x + 3=\pm9 $$

Step3: Solve for \(x\)

We now solve for \(x\) in two cases.

Case 1: Positive root
If \(x + 3=9\), we subtract 3 from both sides:

$$ x=9 - 3=6 $$

Case 2: Negative root
If \(x + 3=- 9\), we subtract 3 from both sides:

$$ x=-9 - 3=-12 $$

Answer:

The solutions are \(x = 6\) and \(x=-12\)