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