Evaluate
-5x^{2}+10\sqrt{5}x-25
Factor
5\left(-x^{2}+2\sqrt{5}x-5\right)
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\left(5-\sqrt{5}x\right)\sqrt{5}x-5\left(5-\sqrt{5}x\right)
Use the distributive property to multiply 5-\sqrt{5}x by \sqrt{5}x-5.
\left(5\sqrt{5}-x\left(\sqrt{5}\right)^{2}\right)x-5\left(5-\sqrt{5}x\right)
Use the distributive property to multiply 5-\sqrt{5}x by \sqrt{5}.
\left(5\sqrt{5}-x\times 5\right)x-5\left(5-\sqrt{5}x\right)
The square of \sqrt{5} is 5.
\left(5\sqrt{5}-5x\right)x-5\left(5-\sqrt{5}x\right)
Multiply -1 and 5 to get -5.
5\sqrt{5}x-5x^{2}-5\left(5-\sqrt{5}x\right)
Use the distributive property to multiply 5\sqrt{5}-5x by x.
5\sqrt{5}x-5x^{2}-25+5\sqrt{5}x
Use the distributive property to multiply -5 by 5-\sqrt{5}x.
10\sqrt{5}x-5x^{2}-25
Combine 5\sqrt{5}x and 5\sqrt{5}x to get 10\sqrt{5}x.
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}