If `x < 0` and y is 5 more than the square of x, which one of the following expresses x in terms of y?

Options

A. `x = sqrt(y - 5)`
B. `x = -sqrt(y - 5)`
C. `x = sqrt(y - 5)`
D. `x = sqrt(y^2 - 5)`

Answer

To express \( x \) in terms of \( y \), we start with the information given in the problem.

1. **Understanding the relationship between \( x \) and \( y \)**:
We know that \( y \) is 5 more than the square of \( x \). This can be mathematically expressed as:
\[ y = x^2 + 5 \]

2. **Rearranging the equation to isolate \( x^2 \)**:
We want to express \( x \) in terms of \( y \), so we first isolate \( x^2 \):
\[ x^2 = y - 5 \]

3. **Taking the square root of both sides**:
To solve for \( x \), we take the square root of both sides:
\[ x = \pm \sqrt{y - 5} \]

4. **Considering the condition \( x < 0 \)**:
Since we are given that \( x < 0 \), we only consider the negative root:
\[ x = -\sqrt{y - 5} \]

Thus, the expression for \( x \) in terms of \( y \) is:
\[ x = -\sqrt{y - 5} \]