Solve for x
x=\frac{y^{2}+1}{5}
y\geq 0
Solve for x (complex solution)
x=\frac{y^{2}+1}{5}
arg(y)<\pi \text{ or }y=0
Solve for y
y=\sqrt{5x-1}
x\geq \frac{1}{5}
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\sqrt{5x-1}=y
Swap sides so that all variable terms are on the left hand side.
5x-1=y^{2}
Square both sides of the equation.
5x-1-\left(-1\right)=y^{2}-\left(-1\right)
Add 1 to both sides of the equation.
5x=y^{2}-\left(-1\right)
Subtracting -1 from itself leaves 0.
5x=y^{2}+1
Subtract -1 from y^{2}.
\frac{5x}{5}=\frac{y^{2}+1}{5}
Divide both sides by 5.
x=\frac{y^{2}+1}{5}
Dividing by 5 undoes the multiplication by 5.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}