Solve for x
x=\frac{\left(-\sqrt{4y+4\sqrt{y}-3}+1\right)^{2}}{4}
\left(-\frac{-\sqrt{4y+4\sqrt{y}-3}+1}{2}\geq 0\text{ and }\frac{\sqrt{4y+4\sqrt{y}-3}}{2}+\sqrt{\sqrt{y}-1}\geq \frac{1}{2}\text{ and }\frac{\sqrt{4y+4\sqrt{y}-3}}{2}-\sqrt{\sqrt{y}-1}\leq \frac{1}{2}\text{ and }y\geq 1\right)\text{ or }\left(\frac{-\sqrt{4y+4\sqrt{y}-3}+1}{2}\geq 0\text{ and }-\left(\frac{\sqrt{4y+4\sqrt{y}-3}}{2}-\sqrt{\sqrt{y}-1}\right)\geq -\frac{1}{2}\text{ and }-\left(\frac{\sqrt{4y+4\sqrt{y}-3}}{2}+\sqrt{\sqrt{y}-1}\right)\leq -\frac{1}{2}\text{ and }y\geq 1\right)
Solve for y
y=\frac{\left(-\sqrt{4x+4\sqrt{x}+5}+1\right)^{2}}{4}
x\geq 0\text{ and }-\frac{-\sqrt{4x+4\sqrt{x}+5}+1}{2}\geq 0\text{ and }-x+\frac{\sqrt{4x+4\sqrt{x}+5}}{2}\geq \frac{3}{2}
Share
Copied to clipboard
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}