Solve x^2 \sqrt 60x-15=0

Evaluate

x^{2} 60 x - 15 = 0

Find the domain

More Steps

x^{2} 60 x - 15 = 0, x \geq 0

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

x^{2} 60 x = 15

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

(x^{2} 60 x)^{2} = 1 5^{2}

Evaluate the power

60 x^{5} = 225

Divide both sides

\frac{60 x ^{5}}{60} = \frac{225}{60}

Divide the numbers

x^{5} = \frac{225}{60}

Cancel out the common factor 15

x^{5} = \frac{15}{4}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{15}{4}

Calculate

x = 5 \frac{15}{4}

Simplify the root

More Steps

x = \frac{5 120}{2}

Check if the solution is in the defined range

x = \frac{5 120}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = \frac{5 120}{2}

Solution

More Steps

x = \frac{5 120}{2}

Alternative Form

x \approx 1.302586

Solve the equation