Solve 2x^2=5\sqrt x

Evaluate

2 x^{2} = 5 x

Find the domain

2 x^{2} = 5 x, x \geq 0

Swap the sides

5 x = 2 x^{2}

Rewrite the expression

x = \frac{2 x ^{2}}{5}

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

(x)^{2} = (\frac{2 x ^{2}}{5})^{2}

Evaluate the power

x = \frac{4 x ^{4}}{25}

Cross multiply

x \times 25 = 4 x^{4}

Simplify the equation

25 x = 4 x^{4}

Add or subtract both sides

25 x - 4 x^{4} = 0

Factor the expression

x (25 - 4 x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 25 - 4 x^{3} = 0

Solve the equation

More Steps

x = 0 x = \frac{3 50}{2}

Check if the solution is in the defined range

x = 0 x = \frac{3 50}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = \frac{3 50}{2}

Check the solution

More Steps

x = 0 x = \frac{3 50}{2}

Check the solution

More Steps

x = 0 x = \frac{3 50}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 50}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.842016

Solve the equation