Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each quadratic equation with its solution set.
2x2 − 32 = 0
4x2 − 100 = 0
x2 − 55 = 9
x2 − 140 = -19
2x2 − 18 = 0
{-8, 8}
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{-4, 4}
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{-5, 5}
arrowRight
{-11, 11}
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Answer 1

Let's solve each quadratic equation one by one to find their solution sets:

1. **\(2x^2 - 32 = 0\)**
- \(2x^2 = 32\)
- \(x^2 = 16\)
- \(x = \pm 4\)
- **Solution set: \{-4, 4\}**

2. **\(4x^2 - 100 = 0\)**
- \(4x^2 = 100\)
- \(x^2 = 25\)
- \(x = \pm 5\)
- **Solution set: \{-5, 5\}**

3. **\(x^2 - 55 = 9\)**
- \(x^2 - 64 = 0\)
- \(x^2 = 64\)
- \(x = \pm 8\)
- **Solution set: \{-8, 8\}**

4. **\(x^2 - 140 = -19\)**
- \(x^2 - 121 = 0\)
- \(x^2 = 121\)
- \(x = \pm 11\)
- **Solution set: \{-11, 11\}**

5. **\(2x^2 - 18 = 0\)**
- \(2x^2 = 18\)
- \(x^2 = 9\)
- \(x = \pm 3\)
- **Solution set: \{ -3, 3 \}** (Not in the pairs given)

Now, let's match each equation with its solution set:

- **\(2x^2 - 32 = 0\)** → **\{-4, 4\}**
- **\(4x^2 - 100 = 0\)** → **\{-5, 5\}**
- **\(x^2 - 55 = 9\)** → **\{-8, 8\}**
- **\(x^2 - 140 = -19\)** → **\{-11, 11\}**

Thus, the matches are:

- \(2x^2 - 32 = 0\) → \{-4, 4\}
- \(4x^2 - 100 = 0\) → \{-5, 5\}
- \(x^2 - 55 = 9\) → \{-8, 8\}
- \(x^2 - 140 = -19\) → \{-11, 11\}

The last equation \(2x^2 - 18 = 0\) gives \{±3\}, which is not used in the answer choices given.

So, the final matches are:

- \(2x^2 - 32 = 0\) → \{-4, 4\}
- \(4x^2 - 100 = 0\) → \{-5, 5\}
- \(x^2 - 55 = 9\) → \{-8, 8\}
- \(x^2 - 140 = -19\) → \{-11, 11\}