To find the value of the expression [tex]\(\frac{2 x^2}{x} + x(100 - 15x)\)[/tex] when [tex]\(x = 5\)[/tex], we will evaluate each term in the expression step-by-step.
1. Start by substituting [tex]\(x = 5\)[/tex] into the first term:
[tex]\[
\frac{2 x^2}{x}
\][/tex]
Replacing [tex]\(x\)[/tex] with 5:
[tex]\[
\frac{2 \cdot 5^2}{5}
\][/tex]
Calculate [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
Now, multiply by 2:
[tex]\[
2 \cdot 25 = 50
\][/tex]
Finally, divide by 5:
[tex]\[
\frac{50}{5} = 10
\][/tex]
So, the first term when [tex]\(x = 5\)[/tex] is 10.
2. Next, substitute [tex]\(x = 5\)[/tex] into the second term:
[tex]\[
x(100 - 15x)
\][/tex]
Replacing [tex]\(x\)[/tex] with 5:
[tex]\[
5(100 - 15 \cdot 5)
\][/tex]
First, calculate the multiplication inside the parentheses:
[tex]\[
15 \cdot 5 = 75
\][/tex]
Now, subtract from 100:
[tex]\[
100 - 75 = 25
\][/tex]
Finally, multiply by 5:
[tex]\[
5 \cdot 25 = 125
\][/tex]
So, the second term when [tex]\(x = 5\)[/tex] is 125.
3. To find the total value of the expression, sum the first and second terms:
[tex]\[
10 + 125
\][/tex]
This gives:
[tex]\[
10 + 125 = 135
\][/tex]
Therefore, the value of the expression [tex]\(\frac{2 x^2}{x} + x(100 - 15x)\)[/tex] when [tex]\(x = 5\)[/tex] is [tex]\(\boxed{135}\)[/tex].
