Solve for x
x=0
x=\frac{1}{9}\approx 0.111111111
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\left(3x\right)^{2}=\left(\sqrt{x}\right)^{2}
Square both sides of the equation.
3^{2}x^{2}=\left(\sqrt{x}\right)^{2}
Expand \left(3x\right)^{2}.
9x^{2}=\left(\sqrt{x}\right)^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}=x
Calculate \sqrt{x} to the power of 2 and get x.
9x^{2}-x=0
Subtract x from both sides.
x\left(9x-1\right)=0
Factor out x.
x=0 x=\frac{1}{9}
To find equation solutions, solve x=0 and 9x-1=0.
3\times 0=\sqrt{0}
Substitute 0 for x in the equation 3x=\sqrt{x}.
0=0
Simplify. The value x=0 satisfies the equation.
3\times \frac{1}{9}=\sqrt{\frac{1}{9}}
Substitute \frac{1}{9} for x in the equation 3x=\sqrt{x}.
\frac{1}{3}=\frac{1}{3}
Simplify. The value x=\frac{1}{9} satisfies the equation.
x=0 x=\frac{1}{9}
List all solutions of 3x=\sqrt{x}.
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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}