AI Solution

Dividing the whole equation by 2 is a legal algebraic operation because you are multiplying both sides of the equation by the same non‑zero number (the reciprocal of 2).

If the original equation is

2x^{2}-8x+6=0,

and you divide every term on the left‑hand side (including the constant term) by 2, you get

\frac{2x^{2}}{2}-\frac{8x}{2}+\frac{6}{2}=0\;\Longrightarrow\;x^{2}-4x+3=0.

The right‑hand side stays 0 because $0/2 = 0$ .

Since you performed the same operation on each term, the set of numbers that satisfy the new, simpler equation is exactly the same as the set that satisfies the original one. In other words, the roots are unchanged, but the coefficients are smaller, which makes factoring or applying the quadratic formula easier and reduces the chance of arithmetic errors.

Key point: you must divide all terms (including the constant) by the same factor. If you only divided part of the equation, the balance would be broken and the solutions would change.

Tewtor.ai

QProblem

ASolution

Need help with your own problems?