Solve 6sqrt{x-2}=4sqrt{x+8}

$$6 \sqrt { x - 2 } = 4 \sqrt { x + 8 }$$

Solve for x

$$x=10$$

Solution Steps

Square both sides of the equation.

$$\left(6\sqrt{x-2}\right)^{2}=\left(4\sqrt{x+8}\right)^{2}$$

Expand \left(6\sqrt{x-2}\right)^{2}.

$$6^{2}\left(\sqrt{x-2}\right)^{2}=\left(4\sqrt{x+8}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{x-2}\right)^{2}=\left(4\sqrt{x+8}\right)^{2}$$

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

$$36\left(x-2\right)=\left(4\sqrt{x+8}\right)^{2}$$

Use the distributive property to multiply 36 by x-2.

$$36x-72=\left(4\sqrt{x+8}\right)^{2}$$

Expand \left(4\sqrt{x+8}\right)^{2}.

$$36x-72=4^{2}\left(\sqrt{x+8}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$36x-72=16\left(\sqrt{x+8}\right)^{2}$$

Calculate \sqrt{x+8} to the power of 2 and get x+8.

$$36x-72=16\left(x+8\right)$$

Use the distributive property to multiply 16 by x+8.

$$36x-72=16x+128$$

Subtract 16x from both sides.

$$36x-72-16x=128$$

Combine 36x and -16x to get 20x.

$$20x-72=128$$

Add 72 to both sides.

$$20x=128+72$$

Add 128 and 72 to get 200.

$$20x=200$$

Divide both sides by 20.

$$x=\frac{200}{20}$$

Divide 200 by 20 to get 10.

$$x=10$$

Substitute 10 for x in the equation 6\sqrt{x-2}=4\sqrt{x+8}.

$$6\sqrt{10-2}=4\sqrt{10+8}$$

Simplify. The value x=10 satisfies the equation.

$$12\times 2^{\frac{1}{2}}=12\times 2^{\frac{1}{2}}$$

Equation 6\sqrt{x-2}=4\sqrt{x+8} has a unique solution.

$$x=10$$