To make \( y \) the subject of the equation \( x = y^2 + 5z \), follow these steps:

### Given equation:
\[
x = y^2 + 5z
\]

1. Subtract \( 5z \) from both sides:
\[
x - 5z = y^2
\]

2. Take the square root of both sides:
\[
y = \pm \sqrt{x - 5z}
\]

Thus, the equation becomes:
\[
y = \pm \sqrt{x - 5z}
\]

Would you like further details or have any questions?

Here are 5 related questions to practice:
1. Solve for \( z \) in the equation \( x = y^2 + 5z \).
2. What is the value of \( y \) if \( x = 25 \) and \( z = 2 \)?
3. Rewrite \( y = \sqrt{x - 5z} \) as an absolute value equation.
4. If \( y^2 = a \), how do you express \( y \) in terms of \( a \)?
5. Find the derivative of \( y = \sqrt{x - 5z} \) with respect to \( x \).

**Tip**: Always remember that taking the square root introduces both positive and negative roots, so you often have \( \pm \sqrt{} \).

Learn how to solve the equation x = y^2 + 5z by making y the subject. This step-by-step guide covers key algebraic concepts such as rearranging formulas and applying the square root. Suitable for high school students in Grades 9-12.

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