To find the equation that best represents the standard form of the expression [tex]\(\frac{x^2}{2} = 7x\)[/tex], we need to convert it into a standard quadratic form, which is [tex]\(ax^2 + bx + c = 0\)[/tex].
Let's go through the steps carefully:
1. Original Equation:
[tex]\[
\frac{x^2}{2} = 7x
\][/tex]
2. Eliminate the Fraction:
Multiply both sides by 2 to clear the fraction:
[tex]\[
2 \cdot \left(\frac{x^2}{2}\right) = 2 \cdot 7x
\][/tex]
This simplifies to:
[tex]\[
x^2 = 14x
\][/tex]
3. Move All Terms to One Side:
Subtract [tex]\(14x\)[/tex] from both sides to set the equation to 0:
[tex]\[
x^2 - 14x = 0
\][/tex]
4. Final Standard Form:
The resulting equation is in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex]:
[tex]\[
x^2 - 14x = 0
\][/tex]
Therefore, the equation that best represents the standard form of [tex]\(\frac{x^2}{2} = 7x\)[/tex] is:
[tex]\[
\boxed{x^2 - 14x = 0}
\][/tex]
