Solve sqrt{3x-1}=2sqrt{x+2}

$$\sqrt { 3 x - 1 } = 2 \sqrt { x + 2 }$$

Solve for x (complex solution)

$$x=-9$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3x-1}\right)^{2}=\left(2\sqrt{x+2}\right)^{2}$$

Calculate \sqrt{3x-1} to the power of 2 and get 3x-1.

$$3x-1=\left(2\sqrt{x+2}\right)^{2}$$

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

$$3x-1=2^{2}\left(\sqrt{x+2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$3x-1=4\left(\sqrt{x+2}\right)^{2}$$

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

$$3x-1=4\left(x+2\right)$$

Use the distributive property to multiply 4 by x+2.

$$3x-1=4x+8$$

Subtract 4x from both sides.

$$3x-1-4x=8$$

Combine 3x and -4x to get -x.

$$-x-1=8$$

Add 1 to both sides.

$$-x=8+1$$

Add 8 and 1 to get 9.

$$-x=9$$

Multiply both sides by -1.

$$x=-9$$

Substitute -9 for x in the equation \sqrt{3x-1}=2\sqrt{x+2}.

$$\sqrt{3\left(-9\right)-1}=2\sqrt{-9+2}$$

Simplify. The value x=-9 satisfies the equation.

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

Equation \sqrt{3x-1}=2\sqrt{x+2} has a unique solution.

$$x=-9$$