Solve for g (complex solution)
\left\{\begin{matrix}g=-\frac{p_{x}-p_{y}}{hp}\text{, }&h\neq 0\text{ and }p\neq 0\\g\in \mathrm{C}\text{, }&p_{x}=p_{y}\text{ and }\left(h=0\text{ or }p=0\right)\end{matrix}\right.
Solve for h (complex solution)
\left\{\begin{matrix}h=-\frac{p_{x}-p_{y}}{gp}\text{, }&g\neq 0\text{ and }p\neq 0\\h\in \mathrm{C}\text{, }&p_{x}=p_{y}\text{ and }\left(g=0\text{ or }p=0\right)\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=-\frac{p_{x}-p_{y}}{hp}\text{, }&h\neq 0\text{ and }p\neq 0\\g\in \mathrm{R}\text{, }&p_{x}=p_{y}\text{ and }\left(h=0\text{ or }p=0\right)\end{matrix}\right.
Solve for h
\left\{\begin{matrix}h=-\frac{p_{x}-p_{y}}{gp}\text{, }&g\neq 0\text{ and }p\neq 0\\h\in \mathrm{R}\text{, }&p_{x}=p_{y}\text{ and }\left(g=0\text{ or }p=0\right)\end{matrix}\right.
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p_{x}+\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}
Anything plus zero gives itself.
\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}
Subtract p_{x} from both sides.
pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}-\frac{1}{2}pv^{2}
Subtract \frac{1}{2}pv^{2} from both sides.
pgh=p_{y}-p_{x}
Combine \frac{1}{2}pv^{2} and -\frac{1}{2}pv^{2} to get 0.
hpg=p_{y}-p_{x}
The equation is in standard form.
\frac{hpg}{hp}=\frac{p_{y}-p_{x}}{hp}
Divide both sides by ph.
g=\frac{p_{y}-p_{x}}{hp}
Dividing by ph undoes the multiplication by ph.
p_{x}+\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}
Anything plus zero gives itself.
\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}
Subtract p_{x} from both sides.
pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}-\frac{1}{2}pv^{2}
Subtract \frac{1}{2}pv^{2} from both sides.
pgh=p_{y}-p_{x}
Combine \frac{1}{2}pv^{2} and -\frac{1}{2}pv^{2} to get 0.
gph=p_{y}-p_{x}
The equation is in standard form.
\frac{gph}{gp}=\frac{p_{y}-p_{x}}{gp}
Divide both sides by pg.
h=\frac{p_{y}-p_{x}}{gp}
Dividing by pg undoes the multiplication by pg.
p_{x}+\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}
Anything plus zero gives itself.
\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}
Subtract p_{x} from both sides.
pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}-\frac{1}{2}pv^{2}
Subtract \frac{1}{2}pv^{2} from both sides.
pgh=p_{y}-p_{x}
Combine \frac{1}{2}pv^{2} and -\frac{1}{2}pv^{2} to get 0.
hpg=p_{y}-p_{x}
The equation is in standard form.
\frac{hpg}{hp}=\frac{p_{y}-p_{x}}{hp}
Divide both sides by ph.
g=\frac{p_{y}-p_{x}}{hp}
Dividing by ph undoes the multiplication by ph.
p_{x}+\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}
Anything plus zero gives itself.
\frac{1}{2}pv^{2}+pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}
Subtract p_{x} from both sides.
pgh=p_{y}+\frac{1}{2}pv^{2}-p_{x}-\frac{1}{2}pv^{2}
Subtract \frac{1}{2}pv^{2} from both sides.
pgh=p_{y}-p_{x}
Combine \frac{1}{2}pv^{2} and -\frac{1}{2}pv^{2} to get 0.
gph=p_{y}-p_{x}
The equation is in standard form.
\frac{gph}{gp}=\frac{p_{y}-p_{x}}{gp}
Divide both sides by pg.
h=\frac{p_{y}-p_{x}}{gp}
Dividing by pg undoes the multiplication by pg.
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Matrix
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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
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