Evaluate
-\frac{x^{2}}{4}+1
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-\frac{x^{2}}{4}+1
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\frac{1}{2}x\left(-\frac{1}{2}\right)x+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Apply the distributive property by multiplying each term of \frac{1}{2}x-1 by each term of -\frac{1}{2}x-1.
\frac{1}{2}x^{2}\left(-\frac{1}{2}\right)+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Multiply x and x to get x^{2}.
\frac{1\left(-1\right)}{2\times 2}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Multiply \frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{-1}{4}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 2}.
-\frac{1}{4}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.
-\frac{1}{4}x^{2}-\frac{1}{2}x-\left(-\frac{1}{2}x\right)+1
Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.
-\frac{1}{4}x^{2}-\frac{1}{2}x+\frac{1}{2}x+1
Multiply -1 and -\frac{1}{2} to get \frac{1}{2}.
-\frac{1}{4}x^{2}+1
Combine -\frac{1}{2}x and \frac{1}{2}x to get 0.
\frac{1}{2}x\left(-\frac{1}{2}\right)x+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Apply the distributive property by multiplying each term of \frac{1}{2}x-1 by each term of -\frac{1}{2}x-1.
\frac{1}{2}x^{2}\left(-\frac{1}{2}\right)+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Multiply x and x to get x^{2}.
\frac{1\left(-1\right)}{2\times 2}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Multiply \frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{-1}{4}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 2}.
-\frac{1}{4}x^{2}+\frac{1}{2}x\left(-1\right)-\left(-\frac{1}{2}x\right)+1
Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.
-\frac{1}{4}x^{2}-\frac{1}{2}x-\left(-\frac{1}{2}x\right)+1
Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.
-\frac{1}{4}x^{2}-\frac{1}{2}x+\frac{1}{2}x+1
Multiply -1 and -\frac{1}{2} to get \frac{1}{2}.
-\frac{1}{4}x^{2}+1
Combine -\frac{1}{2}x and \frac{1}{2}x to get 0.
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}