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Question
Simplify the following:
x2 − 3x + 5 − \[\frac{1}{2}\] (3x2 − 5x + 7)
Solution
\[ x^2 - 3x + 5 - \frac{1}{2}\left( 3 x^2 - 5x + 7 \right)\]
\[ = x^2 - 3x + 5 - \frac{3 x^2}{2} + \frac{5x}{2} - \frac{7}{2}\]
\[ = x^2 - \frac{3 x^2}{2} - 3x + \frac{5x}{2} + 5 - \frac{7}{2} (\text { Collecting like terms })\]
\[ = \left( \frac{1 - 3}{2} \right) x^2 + \left( \frac{- 3 + 5}{2} \right)x + \left( \frac{10 - 7}{2} \right)\]
\[ = - \frac{x^2}{2} - \frac{x}{2} + \frac{3}{2}\]
Thus, the answer is \[- \frac{x^2}{2} - \frac{x}{2} + \frac{3}{2}\].
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