Solve sqrt{3w+14}=sqrt{5w+2}

$$\sqrt { 3 w + 14 } = \sqrt { 5 w + 2 }$$

Solve for w

$$w=6$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3w+14}\right)^{2}=\left(\sqrt{5w+2}\right)^{2}$$

Calculate \sqrt{3w+14} to the power of 2 and get 3w+14.

$$3w+14=\left(\sqrt{5w+2}\right)^{2}$$

Calculate \sqrt{5w+2} to the power of 2 and get 5w+2.

$$3w+14=5w+2$$

Subtract 5w from both sides.

$$3w+14-5w=2$$

Combine 3w and -5w to get -2w.

$$-2w+14=2$$

Subtract 14 from both sides.

$$-2w=2-14$$

Subtract 14 from 2 to get -12.

$$-2w=-12$$

Divide both sides by -2.

$$w=\frac{-12}{-2}$$

Divide -12 by -2 to get 6.

$$w=6$$

Substitute 6 for w in the equation \sqrt{3w+14}=\sqrt{5w+2}.

$$\sqrt{3\times 6+14}=\sqrt{5\times 6+2}$$

Simplify. The value w=6 satisfies the equation.

$$4\times 2^{\frac{1}{2}}=4\times 2^{\frac{1}{2}}$$

Equation \sqrt{3w+14}=\sqrt{5w+2} has a unique solution.

$$w=6$$