Solve by Factoring x^2 = square root of x

Problem

x2=√(,x)

Solution

1. Set the equation to zero by subtracting √(,x) from both sides to prepare for factoring.

x2−√(,x)=0

2. Rewrite the radical using a fractional exponent to make it easier to identify common factors.

x2−x(1/2)=0

3. Factor out the greatest common factor, which is x(1/2)

x(1/2)*(x(3/2)−1)=0

4. Apply the zero product property by setting each factor equal to zero.

x(1/2)=0

x(3/2)−1=0

5. Solve for x in the first equation by squaring both sides.

x=0

6. Solve for x in the second equation by isolating the variable and raising both sides to the reciprocal power.

x(3/2)=1

(x(3/2))(2/3)=1(2/3)

x=1

7. Verify the solutions in the original equation to ensure they are valid and not extraneous.

0=√(,0)⇒0=0

1=√(,1)⇒1=1

Final Answer

x=0,1

Want more problems? Check here!