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You have shared an image with a mathematical problem involving a function \( g(x) = x^2 - 5 \), and it asks for the values of \( x \) where:

1. \( g(x) = 20 \)
2. \( g(x) = 6 \)

Let's break it down:

### a. \( g(x) = 20 \)
The equation to solve is:
\[
x^2 - 5 = 20
\]
Adding 5 to both sides:
\[
x^2 = 25
\]
Taking the square root of both sides:
\[
x = \pm 5
\]
So, the solution is \( x = 5 \) or \( x = -5 \).

### b. \( g(x) = 6 \)
The equation to solve is:
\[
x^2 - 5 = 6
\]
Adding 5 to both sides:
\[
x^2 = 11
\]
Taking the square root of both sides:
\[
x = \pm \sqrt{11}
\]
Thus, the solutions are \( x = \sqrt{11} \) or \( x = -\sqrt{11} \).

Would you like further details or explanations on any steps?

Here are 5 related questions you might find useful:

1. How do we handle equations involving higher powers of \( x \) (e.g., cubic equations)?
2. What is the general method to solve quadratic equations?
3. How does completing the square work to solve quadratic equations?
4. What is the significance of the discriminant in quadratic equations?
5. How would these solutions change if the equation were \( g(x) = x^2 + c \)?

**Tip**: Always remember to check both positive and negative roots when solving equations involving squares.

If g(x) = x^2 - 5, find the value(s) of x so that g(x) = 20 and g(x) = 6.

Learn how to solve quadratic function g(x) = x^2 - 5 for specific values g(x) = 20 and g(x) = 6. This problem covers fundamental algebraic concepts, including solving quadratic equations with two solutions. Suitable for students in Grades 7-10.

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