Find the zeros of the function. Enter the solutions from least to greatest.
\[f(x) = (x - 10)^2 - 49\]

To find the zeros of the function \( f(x) = (x - 10)^2 - 49 \), we need to solve the equation \( f(x) = 0 \). This means we set the function equal to zero and solve for \( x \).

\[
(x - 10)^2 - 49 = 0
\]

First, add 49 to both sides of the equation:

\[
(x - 10)^2 = 49
\]

Next, take the square root of both sides:

\[
x - 10 = \pm \sqrt{49}
\]

Since \(\sqrt{49} = 7\), we have:

\[
x - 10 = \pm 7
\]

This gives us two possible equations:

1. \(x - 10 = 7\)
2. \(x - 10 = -7\)

Solve each equation:

1. \(x = 7 + 10 = 17\)
2. \(x = -7 + 10 = 3\)

So, the zeros of the function are \(x = 3\) and \(x = 17\).

Thus, the solutions from least to greatest are:
\[
\boxed{3 \text{ and } 17}
\]

Would you like any details or have any questions? 

Here are five related questions for further practice:

1. Find the zeros of \(f(x) = (x + 5)^2 - 16\).
2. Solve the equation \( (x - 4)^2 - 25 = 0 \).
3. Determine the zeros of the function \( g(x) = (x - 2)^2 - 36 \).
4. Find the solutions to the equation \( h(x) = (x + 8)^2 - 64 \).
5. Solve for \(x\) in \( (x - 1)^2 - 9 = 0 \).

**Tip:** Always remember that taking the square root of both sides of an equation introduces both the positive and negative roots.

Learn how to find the zeros of the function (x - 10)^2 - 49 step-by-step with a detailed solution. This problem involves solving a quadratic equation, using the square root property, and understanding function zeros. Suitable for high school students in Grades 9-12.

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