To solve the equation ( 1 2x2 = 3x ), we first need to move all terms to one side to form a quadratic equation. We can do this by adding ( 2x2 ) to both sides and subtracting ( 3x ) from both sides:
[
1 2x2 + 2x2 3x = 3x 3x
]
This simplifies to:
[
1 3x = 0
]
Now we have a linear equation, which we can solve for ( x ):
[
-3x = -1
]
Divide both sides by ( -3 ) to solve for ( x ):
[
x = frac{-1
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