Solve x^3/2-\sqrt x^3 x^2

Evaluate

\frac{x ^{3}}{2} - (x)^{3} x^{2}

To find the roots of the expression,set the expression equal to 0

\frac{x ^{3}}{2} - (x)^{3} x^{2} = 0

Find the domain

\frac{x ^{3}}{2} - (x)^{3} x^{2} = 0, x \geq 0

Calculate

\frac{x ^{3}}{2} - (x)^{3} x^{2} = 0

Multiply the terms

More Steps

\frac{x ^{3}}{2} - x^{3} x = 0

Subtract the terms

More Steps

\frac{x ^{3} - 2 x ^{3} x}{2} = 0

Simplify

x^{3} - 2 x^{3} x = 0

Move the expression to the right-hand side and change its sign

- 2 x^{3} x = - x^{3}

Divide both sides of the equation by - 1

2 x^{3} x = x^{3}

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(2 x^{3} x)^{2} = (x^{3})^{2}

Evaluate the power

4 x^{7} = x^{6}

Move the expression to the left side

4 x^{7} - x^{6} = 0

Factor the expression

x^{6} (4 x - 1) = 0

Separate the equation into 2 possible cases

x^{6} = 0 4 x - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 4 x - 1 = 0

Solve the equation

More Steps

x = 0 x = \frac{1}{4}

Check if the solution is in the defined range

x = 0 x = \frac{1}{4}, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = \frac{1}{4}

Solution

x_{1} = 0, x_{2} = \frac{1}{4}

Alternative Form

x_{1} = 0, x_{2} = 0.25

Simplify the expression