2. Solve x2=289

Question

by inspection. There are two real solutions. Enter the lesser number first.(2 points)
{
,
}
Question 3
3. Which values are in the solution set of the quadratic equation, −9+(x−3)2−4=−4
? Solve using square roots and choose all that apply.(2 points)
Responses

16
16

28
28

-8
-8

8
8

2
2

-22
-22

-10
-10

-2

Answer 1

Question 2: Solve \( x^2 = 289 \) by inspection.

To solve by inspection, recognize that:

\[ x^2 = 289 \implies x = \pm \sqrt{289} \implies x = \pm 17 \]

Thus, the two real solutions are:

\[ {-17, 17} \]

Question 3: Solve the quadratic equation \( -9 + (x-3)^2 - 4 = -4 \)

First, simplify the equation:

\[ -9 + (x-3)^2 - 4 = -4 \]

Combine like terms:

\[ (x - 3)^2 - 13 = -4 \]

Add 13 to both sides:

\[ (x - 3)^2 = 9 \]

Next, take the square root of both sides:

\[ x - 3 = \pm 3 \]

This leads to two equations:

1. \( x - 3 = 3 \)

   • Adding 3 to each side gives: \[ x = 6 \]

2. \( x - 3 = -3 \)

   • Adding 3 to each side gives: \[ x = 0 \]

So, the solutions to the quadratic equation are:

\[ x = 6 \quad \text{and} \quad x = 0 \]

Now, let's look at the possible responses:

• 16
• 28
• -8
• 8
• 2
• -22
• -10
• -2
• 6
• 0

The correct answers from the above response options, based on our solutions, are:

6 and 0.

If only the valid options you provided are presented, and they are not explicitly listed among your choices, then those specific solutions must be retracted since they aren’t part of the given options. Please provide the exact available options or confirm if 6 and 0 are acceptable based on the context of the solution set inquiry.