Solve sqrt{5x-2}=2sqrt{2x-5}

$$\sqrt{ 5x-2 } =2 \sqrt{ 2x-5 }$$

Solve for x

$$x=6$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5x-2}\right)^{2}=\left(2\sqrt{2x-5}\right)^{2}$$

Calculate \sqrt{5x-2} to the power of 2 and get 5x-2.

$$5x-2=\left(2\sqrt{2x-5}\right)^{2}$$

Expand \left(2\sqrt{2x-5}\right)^{2}.

$$5x-2=2^{2}\left(\sqrt{2x-5}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5x-2=4\left(\sqrt{2x-5}\right)^{2}$$

Calculate \sqrt{2x-5} to the power of 2 and get 2x-5.

$$5x-2=4\left(2x-5\right)$$

Use the distributive property to multiply 4 by 2x-5.

$$5x-2=8x-20$$

Subtract 8x from both sides.

$$5x-2-8x=-20$$

Combine 5x and -8x to get -3x.

$$-3x-2=-20$$

Add 2 to both sides.

$$-3x=-20+2$$

Add -20 and 2 to get -18.

$$-3x=-18$$

Divide both sides by -3.

$$x=\frac{-18}{-3}$$

Divide -18 by -3 to get 6.

$$x=6$$

Substitute 6 for x in the equation \sqrt{5x-2}=2\sqrt{2x-5}.

$$\sqrt{5\times 6-2}=2\sqrt{2\times 6-5}$$

Simplify. The value x=6 satisfies the equation.

$$2\times 7^{\frac{1}{2}}=2\times 7^{\frac{1}{2}}$$

Equation \sqrt{5x-2}=2\sqrt{2x-5} has a unique solution.

$$x=6$$