Use inspection to solve the equation x2=36169

Question

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)
Responses

{−613}
{
−
6
13
}
left brace negative Start Fraction 6 over 13 End Fraction right brace

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

{613}
{
6
13
}
left brace Start Fraction 6 over 13 End Fraction right brace

{−613,613}

Answer 1

To solve the equation \( x^2 = 36169 \) by inspection, we can find the square root of both sides of the equation.

Taking the square root, we have:

\[ x = \pm \sqrt{36169} \]

Now, we need to find \( \sqrt{36169} \). By inspection or by calculating, we find that:

\[ \sqrt{36169} = 189 \]

Thus, the solutions to the equation are:

\[ x = 189 \quad \text{and} \quad x = -189 \]

This means the correct solution set is:

{ -189, 189 }

So the correct response is: {−189, 189}.