- Solve the quadratic equation using the squa $$ 9=(x+8)^{2} $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation using the method of taking square roots, follow these steps:

$$
9 = (x + 8)^2
$$

1. **Take the square root of both sides:**

$$
\sqrt{9} = \sqrt{(x + 8)^2}
$$

2. **Simplify the square roots:**

$$
\pm 3 = x + 8
$$

The "$$\pm$$" symbol indicates that there are two possible solutions: one where the square root is positive and one where it is negative.

3. **Solve for $$ x $$ in both cases:**

- **Case 1:** Positive square root

$$
     3 = x + 8
     $$

Subtract 8 from both sides:

$$
     x = 3 - 8 \
     x = -5
     $$

- **Case 2:** Negative square root

$$
     -3 = x + 8
     $$

Subtract 8 from both sides:

$$
     x = -3 - 8 \
     x = -11
     $$

4. **Conclusion:**

The quadratic equation $$ 9 = (x + 8)^2 $$ has two solutions:

$$
   x = -5 \quad \text{and} \quad x = -11
   $$
The solutions to the equation $$ 9 = (x + 8)^2 $$ are $$ x = -5 $$ and $$ x = -11 $$.

Solve the quadratic equation using the squa