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

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

Solve for p

$$p=17$$

Solution Steps

Square both sides of the equation.

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

Expand \left(3\sqrt{p-1}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Use the distributive property to multiply 9 by p-1.

$$9p-9=\left(2\sqrt{2p+2}\right)^{2}$$

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

$$9p-9=2^{2}\left(\sqrt{2p+2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9p-9=4\left(\sqrt{2p+2}\right)^{2}$$

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

$$9p-9=4\left(2p+2\right)$$

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

$$9p-9=8p+8$$

Subtract 8p from both sides.

$$9p-9-8p=8$$

Combine 9p and -8p to get p.

$$p-9=8$$

Add 9 to both sides.

$$p=8+9$$

Add 8 and 9 to get 17.

$$p=17$$

Substitute 17 for p in the equation 3\sqrt{p-1}=2\sqrt{2p+2}.

$$3\sqrt{17-1}=2\sqrt{2\times 17+2}$$

Simplify. The value p=17 satisfies the equation.

$$12=12$$

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

$$p=17$$