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

Q: What does it mean when there are 'no values' for x?

It means the inequality has no solution. No matter what real number you substitute for x, the expression $ (2x+30)^2 $ will never be less than zero. The solution set is empty.

Q: What if the question asked for when the function equals zero?

Then you'd solve $ (2x+30)^2 = 0 $! This gives $ 2x+30 = 0 $, so $ x = -15 $. But our question asks for when it's less than zero, which never happens.

Q: How can I visualize this function?

The graph of $ y = (2x+30)^2 $ is a parabola opening upward with vertex at (-15, 0). Since it never goes below the x-axis, there are no points where y

Q: Are there any exceptions to the square rule?

No exceptions with real numbers! However, in advanced mathematics with complex numbers, squares can be negative. But for this problem, we're working with real numbers only.

Quadratic Functions with Square Properties

Look at the function below:

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

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

$f(x) < 0$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the function below:

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

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

$f(x) < 0$

Step-by-step solution

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 $x$

Final Answer

True for no values of $x$

Key Points to Remember

Essential concepts to master this topic

Square Property: Any real number squared is always non-negative
Analysis: $(2x+30)^2 \geq 0$ for all real x values
Verification: Test x = -15: $(2(-15)+30)^2 = 0^2 = 0 \geq 0$ ✓

Common Mistakes

Avoid these frequent errors

Trying to solve the squared expression as a regular equation
Don't set $(2x+30)^2 = 0$ and solve for x = -15! This only finds where the function equals zero, not where it's negative. Since squares are never negative, no solution exists for the inequality $(2x+30)^2 < 0$ . Always remember that squared expressions are always ≥ 0.

Practice Quiz

Test your knowledge with interactive questions

The graph of the function below does not intersect the $$ x $$ -axis.

The parabola's vertex is marked A.

Find all values of $$ x $$ where
$f\left(x\right) > 0$ .

FAQ

Everything you need to know about this question

Why can't a square ever be negative?

When you multiply any real number by itself, the result is always positive or zero. For example: $3^2 = 9$ , $(-3)^2 = 9$ , and $0^2 = 0$ . This is a fundamental property of real numbers!

What does it mean when there are 'no values' for x?

It means the inequality has no solution. No matter what real number you substitute for x, the expression $(2x+30)^2$ will never be less than zero. The solution set is empty.

What if the question asked for when the function equals zero?

Then you'd solve $(2x+30)^2 = 0$ ! This gives $2x+30 = 0$ , so $x = -15$ . But our question asks for when it's less than zero, which never happens.

How can I visualize this function?

The graph of $y = (2x+30)^2$ is a parabola opening upward with vertex at (-15, 0). Since it never goes below the x-axis, there are no points where y < 0.

Are there any exceptions to the square rule?

No exceptions with real numbers! However, in advanced mathematics with complex numbers, squares can be negative. But for this problem, we're working with real numbers only.

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

Quadratic Functions with Square Properties

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't a square ever be negative?

What does it mean when there are 'no values' for x?

What if the question asked for when the function equals zero?

How can I visualize this function?

Are there any exceptions to the square rule?

🌟 Unlock Your Math Potential

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