Solve sqrt{14c-14}=sqrt{4c+6}

$$\sqrt { 14 c - 14 } = \sqrt { 4 c + 6 }$$

Solve for c

$$c=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{14c-14}\right)^{2}=\left(\sqrt{4c+6}\right)^{2}$$

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

$$14c-14=\left(\sqrt{4c+6}\right)^{2}$$

Calculate \sqrt{4c+6} to the power of 2 and get 4c+6.

$$14c-14=4c+6$$

Subtract 4c from both sides.

$$14c-14-4c=6$$

Combine 14c and -4c to get 10c.

$$10c-14=6$$

Add 14 to both sides.

$$10c=6+14$$

Add 6 and 14 to get 20.

$$10c=20$$

Divide both sides by 10.

$$c=\frac{20}{10}$$

Divide 20 by 10 to get 2.

$$c=2$$

Substitute 2 for c in the equation \sqrt{14c-14}=\sqrt{4c+6}.

$$\sqrt{14\times 2-14}=\sqrt{4\times 2+6}$$

Simplify. The value c=2 satisfies the equation.

$$14^{\frac{1}{2}}=14^{\frac{1}{2}}$$

Equation \sqrt{14c-14}=\sqrt{4c+6} has a unique solution.

$$c=2$$