Evaluate
\frac{x^{2}}{2}-\frac{5x}{2}+\frac{9}{8}
Expand
\frac{x^{2}}{2}-\frac{5x}{2}+\frac{9}{8}
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\frac{1}{2}\left(x^{2}-x+\frac{1}{4}\right)-2\left(x-\frac{1}{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}\right)^{2}.
\frac{1}{2}x^{2}-\frac{1}{2}x+\frac{1}{8}-2\left(x-\frac{1}{2}\right)
Use the distributive property to multiply \frac{1}{2} by x^{2}-x+\frac{1}{4}.
\frac{1}{2}x^{2}-\frac{1}{2}x+\frac{1}{8}-2x+1
Use the distributive property to multiply -2 by x-\frac{1}{2}.
\frac{1}{2}x^{2}-\frac{5}{2}x+\frac{1}{8}+1
Combine -\frac{1}{2}x and -2x to get -\frac{5}{2}x.
\frac{1}{2}x^{2}-\frac{5}{2}x+\frac{9}{8}
Add \frac{1}{8} and 1 to get \frac{9}{8}.
\frac{1}{2}\left(x^{2}-x+\frac{1}{4}\right)-2\left(x-\frac{1}{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}\right)^{2}.
\frac{1}{2}x^{2}-\frac{1}{2}x+\frac{1}{8}-2\left(x-\frac{1}{2}\right)
Use the distributive property to multiply \frac{1}{2} by x^{2}-x+\frac{1}{4}.
\frac{1}{2}x^{2}-\frac{1}{2}x+\frac{1}{8}-2x+1
Use the distributive property to multiply -2 by x-\frac{1}{2}.
\frac{1}{2}x^{2}-\frac{5}{2}x+\frac{1}{8}+1
Combine -\frac{1}{2}x and -2x to get -\frac{5}{2}x.
\frac{1}{2}x^{2}-\frac{5}{2}x+\frac{9}{8}
Add \frac{1}{8} and 1 to get \frac{9}{8}.
Examples
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}