Use inspection to solve the equation x^2=36/169 , then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)

Question

Responses

There are no real solutions.

{6/13}

{−6/13}

{−6/13,6/13}

Answer 1

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

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

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

Thus, the solutions to the equation are \(x = \frac{6}{13}\) and \(x = -\frac{6}{13}\).

Therefore, the correct solution set is: \[ {-\frac{6}{13}, \frac{6}{13}} \]

Answer 2

Solve the following quadratic equation using square roots: (x−18)^2=196

Responses

​ {−4,−32}

{214,−178}

{32,4}

{21,5}

Answer 3

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, follow these steps:

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

2. Calculate the square root of 196: \[ \sqrt{196} = 14 \]

3. Set up the equations: \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

4. Solve each equation:

   For the first equation: \[ x - 18 = 14 \implies x = 14 + 18 = 32 \]

   For the second equation: \[ x - 18 = -14 \implies x = -14 + 18 = 4 \]

5. The solutions are: \[ x = 32 \quad \text{and} \quad x = 4 \]

So the correct response is: \({32, 4}\)

Answer 4

Solve the following quadratic equation using square roots: (x+6)^2/2=8

Responses:

{−1.17,−6.83}

{10,−22}

{−2,−10}

​ {−0.34,−11.66}

Answer 5

To solve the quadratic equation \(\frac{(x + 6)^2}{2} = 8\) using square roots, 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: \[ x + 6 = \pm \sqrt{16} \]

3. Calculate the square root: \[ \sqrt{16} = 4 \]

4. Set up the equations: \[ x + 6 = 4 \quad \text{or} \quad x + 6 = -4 \]

5. Solve each equation:

   For the first equation: \[ x + 6 = 4 \implies x = 4 - 6 = -2 \]

   For the second equation: \[ x + 6 = -4 \implies x = -4 - 6 = -10 \]

6. The solutions are: \[ x = -2 \quad \text{and} \quad x = -10 \]

So the correct response is: \({-2, -10}\)

Answer 6

Solve the following quadratic equation using square roots: (x+36)2−38=251

Responses:

{253,−325}

{−19,−53}

{17.84,−13.84}

{53,19}

Answer 7

To solve the quadratic equation \((x + 36)^2 - 38 = 251\) using square roots, follow these steps:

1. Add 38 to both sides to isolate the squared 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: \[ \sqrt{289} = 17 \]

4. Set up the equations: \[ x + 36 = 17 \quad \text{or} \quad x + 36 = -17 \]

5. Solve each equation:

   For the first equation: \[ x + 36 = 17 \implies x = 17 - 36 = -19 \]

   For the second equation: \[ x + 36 = -17 \implies x = -17 - 36 = -53 \]

6. The solutions are: \[ x = -19 \quad \text{and} \quad x = -53 \]

So the correct response is: \({-19, -53}\)