Use inspection to solve the equation x2=196

Question

, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)
Responses

There are no real solutions.
There are no real solutions.

{−14}
left brace negative 14 right brace

{14}
left brace 14 right brace

{−14,14}

Answer 1

To solve the equation \(x^2 = 196\) by inspection, we can take the square root of both sides.

The equation implies that:

\[ x = \sqrt{196} \quad \text{or} \quad x = -\sqrt{196} \]

Calculating the square root gives:

\[ \sqrt{196} = 14 \]

Therefore, the solutions are:

\[ x = 14 \quad \text{and} \quad x = -14 \]

Thus, the correct solution set is:

\[ {-14, 14} \]

So the answer is {−14, 14}.