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

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 2

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 3

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 4

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 5

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 6

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 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: \[ {-19, -53} \]