Evaluate
-\frac{x^{2}}{2}+6x+8
Factor
-\frac{1}{2}\left(x-\left(6-2\sqrt{13}\right)\right)\left(x-\left(2\sqrt{13}+6\right)\right)
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6x+10-2-\frac{x^{2}}{2}
Combine x and 5x to get 6x.
6x+8-\frac{x^{2}}{2}
Subtract 2 from 10 to get 8.
\frac{2\left(6x+8\right)}{2}-\frac{x^{2}}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 6x+8 times \frac{2}{2}.
\frac{2\left(6x+8\right)-x^{2}}{2}
Since \frac{2\left(6x+8\right)}{2} and \frac{x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{12x+16-x^{2}}{2}
Do the multiplications in 2\left(6x+8\right)-x^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}