Solve (2x+30)² < 0: Finding Values When a Square is Negative

Look at the function below:

$y=\left(2x+30\right)^2$

Then determine for which values of $x$ the following is true:

$f(x) < 0$

To solve this problem, we analyze the function $y = (2x + 30)^2$.

Notice that this function involves a squared term, $(2x + 30)$, which is squared to yield the expression $(2x + 30)^2$. A crucial property of squares is that the square of any real number is never negative. Thus, for any real number $z$, $z^2 \geq 0$.

Since $(2x + 30)^2$ is the square of a real expression, it implies that this expression is always greater than or equal to zero. Therefore, it is impossible for $y$ to be less than zero. There are no real values of $x$ that would satisfy the inequality $f(x) < 0$.

Consequently, the correct interpretation is that the inequality $(2x + 30)^2 < 0$ holds true for no values of $x$.

Therefore, the solution to the problem is:

True for no values of $x$