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\left(\sqrt{x}\right)^{2}=\left(\frac{x}{2}\right)^{2}
Square both sides of the equation.
x=\left(\frac{x}{2}\right)^{2}
Calculate \sqrt{x} to the power of 2 and get x.
x=\frac{x^{2}}{2^{2}}
To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.
x=\frac{x^{2}}{4}
Calculate 2 to the power of 2 and get 4.
x-\frac{x^{2}}{4}=0
Subtract \frac{x^{2}}{4} from both sides.
4x-x^{2}=0
Multiply both sides of the equation by 4.
-x^{2}+4x=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-4±\sqrt{4^{2}}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 4 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±4}{2\left(-1\right)}
Take the square root of 4^{2}.
x=\frac{-4±4}{-2}
Multiply 2 times -1.
x=\frac{0}{-2}
Now solve the equation x=\frac{-4±4}{-2} when ± is plus. Add -4 to 4.
x=0
Divide 0 by -2.
x=-\frac{8}{-2}
Now solve the equation x=\frac{-4±4}{-2} when ± is minus. Subtract 4 from -4.
x=4
Divide -8 by -2.
x=0 x=4
The equation is now solved.
\sqrt{0}=\frac{0}{2}
Substitute 0 for x in the equation \sqrt{x}=\frac{x}{2}.
0=0
Simplify. The value x=0 satisfies the equation.
\sqrt{4}=\frac{4}{2}
Substitute 4 for x in the equation \sqrt{x}=\frac{x}{2}.
2=2
Simplify. The value x=4 satisfies the equation.
x=0 x=4
List all solutions of \sqrt{x}=\frac{x}{2}.