Solve the proportion. Write your answer in exact simplest form. Be sure to check your answer.=5.3x21.28

To solve the proportion $5.3 : x = x : 21.28$, we will follow these steps:

1. ### Break Down the Problem

We will express the proportion in a more manageable equation. The proportion can be rewritten as: $\frac{5.3}{x} = \frac{x}{21.28}$

2. ### Relevant Concepts

Using cross-multiplication, we can solve for $x$. According to the property of proportions: $5.3 \cdot 21.28 = x \cdot x$

3. ### Analysis and Detail

Let's calculate the left-hand side: $5.3 \cdot 21.28$

Now perform the multiplication: $5.3 \cdot 21.28 = 113.164$

Now we can set the equation: $x^2 = 113.164$

Taking the square root of both sides gives us: $x = \sqrt{113.164}$

Calculating the square root: $x \approx 10.63$

4. ### Verify and Summarize

To ensure our calculated value is correct, we can check the original proportion with $x \approx 10.63$:

• Left side: $\frac{5.3}{10.63} \approx 0.498$
• Right side: $\frac{10.63}{21.28} \approx 0.498$

Since both sides are approximately equal, our solution holds true.

Final Answer

Thus, the exact simplest form of $x$ is $\sqrt{113.164}$, which approximates to $10.63$.