Question

Use inspection to solve the equation x^2=36/169 , then select the complete solution set below. If there are no real solutions, select “There are no real solutions.”

Answer 1

Use inspection to solve the equation (x-18)^2=196 , then select the complete solution set below. If there are no real solutions, select

Answer 2

Use inspection to solve the equation (x+6)^2/2=8 , then select the complete solution set below. If there are no real solutions, select

Answer 3

Use inspection to solve the equation (x+36)^2-38=251 , then select the complete solution set below. If there are no real solutions, select

Answer 4

To solve the equation \( x^2 = \frac{36}{169} \) using inspection, we can take the square root of both sides:

1. Take the square root:
\[
x = \pm \sqrt{\frac{36}{169}}
\]

2. Simplify the square root:
\[
x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13}
\]

Thus, the complete solution set for the equation \( x^2 = \frac{36}{169} \) is:
\[
x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13}
\]

The complete solution set is:
\[
\left\{ \frac{6}{13}, -\frac{6}{13} \right\}
\]

Answer 5

To solve the equation \( (x - 18)^2 = 196 \) using inspection, we can take the square root of both sides:

1. Take the square root:
\[
x - 18 = \pm \sqrt{196}
\]

2. Simplify the square root:
\[
x - 18 = \pm 14
\]

Now, we can solve for \( x \) by considering both positive and negative scenarios.

**First scenario:**
\[
x - 18 = 14
\]
\[
x = 14 + 18 = 32
\]

**Second scenario:**
\[
x - 18 = -14
\]
\[
x = -14 + 18 = 4
\]

Thus, the complete solution set for the equation \( (x - 18)^2 = 196 \) is:
\[
\{ 32, 4 \}
\]

Answer 6

To solve the equation \(\frac{(x + 6)^2}{2} = 8\) using inspection, we can follow these steps:

1. **Multiply both sides by 2** to eliminate the fraction:
\[
(x + 6)^2 = 16
\]

2. **Take the square root of both sides**:
\[
x + 6 = \pm 4
\]

3. **Solve for \(x\)** by considering both the positive and negative scenarios:

- **First scenario**:
\[
x + 6 = 4
\]
\[
x = 4 - 6 = -2
\]

- **Second scenario**:
\[
x + 6 = -4
\]
\[
x = -4 - 6 = -10
\]

Thus, the complete solution set for the equation \(\frac{(x + 6)^2}{2} = 8\) is:
\[
\{-2, -10\}
\]

Answer 7

To solve the equation \((x + 36)^2 - 38 = 251\) using inspection, we can follow these steps:

1. **Add 38 to both sides** to isolate the square term:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]

3. **Calculate the square root**:
\[
x + 36 = \pm 17
\]

4. **Solve for \(x\)** by considering both the positive and negative scenarios:

- **First scenario**:
\[
x + 36 = 17
\]
\[
x = 17 - 36 = -19
\]

- **Second scenario**:
\[
x + 36 = -17
\]
\[
x = -17 - 36 = -53
\]

Thus, the complete solution set for the equation \((x + 36)^2 - 38 = 251\) is:
\[
\{-19, -53\}
\]