Solve sqrt{5y-14}=sqrt{2y+4}

$$\sqrt { 5 y - 14 } = \sqrt { 2 y + 4 }$$

Solve for y

$$y=6$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5y-14}\right)^{2}=\left(\sqrt{2y+4}\right)^{2}$$

Calculate \sqrt{5y-14} to the power of 2 and get 5y-14.

$$5y-14=\left(\sqrt{2y+4}\right)^{2}$$

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

$$5y-14=2y+4$$

Subtract 2y from both sides.

$$5y-14-2y=4$$

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

$$3y-14=4$$

Add 14 to both sides.

$$3y=4+14$$

Add 4 and 14 to get 18.

$$3y=18$$

Divide both sides by 3.

$$y=\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$y=6$$

Substitute 6 for y in the equation \sqrt{5y-14}=\sqrt{2y+4}.

$$\sqrt{5\times 6-14}=\sqrt{2\times 6+4}$$

Simplify. The value y=6 satisfies the equation.

$$4=4$$

Equation \sqrt{5y-14}=\sqrt{2y+4} has a unique solution.

$$y=6$$