Choose the equation that best represents the standard form of the following expression.

[tex]\[ \frac{x^2}{2}=7x \][/tex]

A. [tex]\(x^2 - 14x = 0\)[/tex]

B. [tex]\(-x^2 + 14x + 0\)[/tex]

C. [tex]\(x^2 + 14x = 0\)[/tex]

D. [tex]\(x^2 - 7x + 2 = 0\)[/tex]



Answer :

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]