Solve for y
y=-3\left(x-2\right)^{2}-5
Solve for x (complex solution)
x=-\frac{\sqrt{-3y-15}}{3}+2
x=\frac{\sqrt{-3y-15}}{3}+2
Solve for x
x=-\frac{\sqrt{-3y-15}}{3}+2
x=\frac{\sqrt{-3y-15}}{3}+2\text{, }y\leq -5
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y=-3\left(x^{2}-4x+4\right)-5
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
y=-3x^{2}+12x-12-5
Use the distributive property to multiply -3 by x^{2}-4x+4.
y=-3x^{2}+12x-17
Subtract 5 from -12 to get -17.
Examples
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Linear equation
y = 3x + 4
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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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