Solve for u
u=-\left(r^{2}+3\right)
Solve for r (complex solution)
r=-i\sqrt{u+3}
r=i\sqrt{u+3}
Solve for r
r=\sqrt{-u-3}
r=-\sqrt{-u-3}\text{, }u\leq -3
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u+3=-r^{2}
Subtract r^{2} from both sides. Anything subtracted from zero gives its negation.
u=-r^{2}-3
Subtract 3 from both sides.
Examples
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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
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