Solve for y
y=-2\left(x+2\right)^{2}+1
Solve for x (complex solution)
x=-\frac{\sqrt{2-2y}}{2}-2
x=\frac{\sqrt{2-2y}}{2}-2
Solve for x
x=-\frac{\sqrt{2-2y}}{2}-2
x=\frac{\sqrt{2-2y}}{2}-2\text{, }y\leq 1
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y=-2\left(x+2\right)^{2}+1
Calculate y to the power of 1 and get y.
y=-2\left(x^{2}+4x+4\right)+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
y=-2x^{2}-8x-8+1
Use the distributive property to multiply -2 by x^{2}+4x+4.
y=-2x^{2}-8x-7
Add -8 and 1 to get -7.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}