Solve for p (complex solution)
\left\{\begin{matrix}p=-\frac{qx-y+r}{x^{2}}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&y=r\text{ and }x=0\end{matrix}\right.
Solve for q (complex solution)
\left\{\begin{matrix}q=-\frac{px^{2}-y+r}{x}\text{, }&x\neq 0\\q\in \mathrm{C}\text{, }&y=r\text{ and }x=0\end{matrix}\right.
Solve for p
\left\{\begin{matrix}p=-\frac{qx-y+r}{x^{2}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&y=r\text{ and }x=0\end{matrix}\right.
Solve for q
\left\{\begin{matrix}q=-\frac{px^{2}-y+r}{x}\text{, }&x\neq 0\\q\in \mathrm{R}\text{, }&y=r\text{ and }x=0\end{matrix}\right.
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px^{2}+qx+r=y
Swap sides so that all variable terms are on the left hand side.
px^{2}+r=y-qx
Subtract qx from both sides.
px^{2}=y-qx-r
Subtract r from both sides.
x^{2}p=-qx+y-r
The equation is in standard form.
\frac{x^{2}p}{x^{2}}=\frac{-qx+y-r}{x^{2}}
Divide both sides by x^{2}.
p=\frac{-qx+y-r}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
px^{2}+qx+r=y
Swap sides so that all variable terms are on the left hand side.
qx+r=y-px^{2}
Subtract px^{2} from both sides.
qx=y-px^{2}-r
Subtract r from both sides.
qx=-px^{2}+y-r
Reorder the terms.
xq=-px^{2}+y-r
The equation is in standard form.
\frac{xq}{x}=\frac{-px^{2}+y-r}{x}
Divide both sides by x.
q=\frac{-px^{2}+y-r}{x}
Dividing by x undoes the multiplication by x.
px^{2}+qx+r=y
Swap sides so that all variable terms are on the left hand side.
px^{2}+r=y-qx
Subtract qx from both sides.
px^{2}=y-qx-r
Subtract r from both sides.
x^{2}p=-qx+y-r
The equation is in standard form.
\frac{x^{2}p}{x^{2}}=\frac{-qx+y-r}{x^{2}}
Divide both sides by x^{2}.
p=\frac{-qx+y-r}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
px^{2}+qx+r=y
Swap sides so that all variable terms are on the left hand side.
qx+r=y-px^{2}
Subtract px^{2} from both sides.
qx=y-px^{2}-r
Subtract r from both sides.
qx=-px^{2}+y-r
Reorder the terms.
xq=-px^{2}+y-r
The equation is in standard form.
\frac{xq}{x}=\frac{-px^{2}+y-r}{x}
Divide both sides by x.
q=\frac{-px^{2}+y-r}{x}
Dividing by x undoes the multiplication by x.
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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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