Solve x^22 \sqrt 2x -6 =0

Evaluate

x^{2} \times 2 2 x - 6 = 0

Find the domain

More Steps

x^{2} \times 2 2 x - 6 = 0, x \geq 0

Use the commutative property to reorder the terms

2 x^{2} 2 x - 6 = 0

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

2 x^{2} 2 x = 6

Divide both sides of the equation by 2

x^{2} 2 x = 3

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

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

Evaluate the power

2 x^{5} = 9

Divide both sides

\frac{2 x ^{5}}{2} = \frac{9}{2}

Divide the numbers

x^{5} = \frac{9}{2}

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

5 x^{5} = 5 \frac{9}{2}

Calculate

x = 5 \frac{9}{2}

Simplify the root

More Steps

x = \frac{5 144}{2}

Check if the solution is in the defined range

x = \frac{5 144}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = \frac{5 144}{2}

Solution

More Steps

x = \frac{5 144}{2}

Alternative Form

x \approx 1.35096

Solve the equation