Type a math problem

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Type a math problem

Evaluate

n^{2}-\frac{13n}{2}+3

$n_{2}−213n +3$

Solution Steps

( n - 6 ) ( n - \frac { 1 } { 2 } )

$(n−6)(n−21 )$

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

Apply the distributive property by multiplying each term of $n−6$ by each term of $n−21 $.

n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

$n_{2}+n(−21 )−6n−6(−21 )$

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

Combine $n(−21 )$ and $−6n$ to get $−213 n$.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

$n_{2}−213 n−6(−21 )$

Express -6\left(-\frac{1}{2}\right)=3 as a single fraction.

Express $−6(−21 )=3$ as a single fraction.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

$n_{2}−213 n+2−6(−1) $

Multiply -6 and -1 to get 6.

Multiply $−6$ and $−1$ to get $6$.

n^{2}-\frac{13}{2}n+\frac{6}{2}

$n_{2}−213 n+26 $

Divide 6 by 2 to get 3.

Divide $6$ by $2$ to get $3$.

n^{2}-\frac{13}{2}n+3

$n_{2}−213 n+3$

Expand

n^{2}-\frac{13n}{2}+3

$n_{2}−213n +3$

Solution Steps

( n - 6 ) ( n - \frac { 1 } { 2 } )

$(n−6)(n−21 )$

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

Apply the distributive property by multiplying each term of $n−6$ by each term of $n−21 $.

n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

$n_{2}+n(−21 )−6n−6(−21 )$

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

Combine $n(−21 )$ and $−6n$ to get $−213 n$.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

$n_{2}−213 n−6(−21 )$

Express -6\left(-\frac{1}{2}\right)=3 as a single fraction.

Express $−6(−21 )=3$ as a single fraction.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

$n_{2}−213 n+2−6(−1) $

Multiply -6 and -1 to get 6.

Multiply $−6$ and $−1$ to get $6$.

n^{2}-\frac{13}{2}n+\frac{6}{2}

$n_{2}−213 n+26 $

Divide 6 by 2 to get 3.

Divide $6$ by $2$ to get $3$.

n^{2}-\frac{13}{2}n+3

$n_{2}−213 n+3$

Factor

\frac{\left(n-6\right)\left(2n-1\right)}{2}

$2(n−6)(2n−1) $

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n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

Express -6\left(-\frac{1}{2}\right)=3 as a single fraction.

n^{2}-\frac{13}{2}n+\frac{6}{2}

Multiply -6 and -1 to get 6.

n^{2}-\frac{13}{2}n+3

Divide 6 by 2 to get 3.

n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

Express -6\left(-\frac{1}{2}\right)=3 as a single fraction.

n^{2}-\frac{13}{2}n+\frac{6}{2}

Multiply -6 and -1 to get 6.

n^{2}-\frac{13}{2}n+3

Divide 6 by 2 to get 3.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

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]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $

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