Solve sqrt{5x-14}-2sqrt{x-1}=0

$$\sqrt{ 5x-14 } -2 \sqrt{ x-1 } = 0$$

Solve for x

$$x=10$$

Solution Steps

Subtract -2\sqrt{x-1} from both sides of the equation.

$$\sqrt{5x-14}=2\sqrt{x-1}$$

Square both sides of the equation.

$$\left(\sqrt{5x-14}\right)^{2}=\left(2\sqrt{x-1}\right)^{2}$$

Calculate \sqrt{5x-14} to the power of 2 and get 5x-14.

$$5x-14=\left(2\sqrt{x-1}\right)^{2}$$

Expand \left(2\sqrt{x-1}\right)^{2}.

$$5x-14=2^{2}\left(\sqrt{x-1}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5x-14=4\left(\sqrt{x-1}\right)^{2}$$

Calculate \sqrt{x-1} to the power of 2 and get x-1.

$$5x-14=4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

$$5x-14=4x-4$$

Subtract 4x from both sides.

$$5x-14-4x=-4$$

Combine 5x and -4x to get x.

$$x-14=-4$$

Add 14 to both sides.

$$x=-4+14$$

Add -4 and 14 to get 10.

$$x=10$$

Substitute 10 for x in the equation \sqrt{5x-14}-2\sqrt{x-1}=0.

$$\sqrt{5\times 10-14}-2\sqrt{10-1}=0$$

Simplify. The value x=10 satisfies the equation.

$$0=0$$

Equation \sqrt{5x-14}=2\sqrt{x-1} has a unique solution.

$$x=10$$