Evaluate
-x^{2}+3x-\frac{5}{2}
Expand
-x^{2}+3x-\frac{5}{2}
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-\left(x^{2}-3x+\frac{9}{4}\right)-\frac{1}{4}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{3}{2}\right)^{2}.
-x^{2}+3x-\frac{9}{4}-\frac{1}{4}
To find the opposite of x^{2}-3x+\frac{9}{4}, find the opposite of each term.
-x^{2}+3x-\frac{5}{2}
Subtract \frac{1}{4} from -\frac{9}{4} to get -\frac{5}{2}.
-\left(x^{2}-3x+\frac{9}{4}\right)-\frac{1}{4}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{3}{2}\right)^{2}.
-x^{2}+3x-\frac{9}{4}-\frac{1}{4}
To find the opposite of x^{2}-3x+\frac{9}{4}, find the opposite of each term.
-x^{2}+3x-\frac{5}{2}
Subtract \frac{1}{4} from -\frac{9}{4} to get -\frac{5}{2}.
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