Solve sqrt{9x-28}=sqrt{5x}

$$\sqrt { 9 x - 28 } = \sqrt { 5 x }$$

Solve for x

$$x=7$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{9x-28}\right)^{2}=\left(\sqrt{5x}\right)^{2}$$

Calculate \sqrt{9x-28} to the power of 2 and get 9x-28.

$$9x-28=\left(\sqrt{5x}\right)^{2}$$

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

$$9x-28=5x$$

Subtract 5x from both sides.

$$9x-28-5x=0$$

Combine 9x and -5x to get 4x.

$$4x-28=0$$

Add 28 to both sides. Anything plus zero gives itself.

$$4x=28$$

Divide both sides by 4.

$$x=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$x=7$$

Substitute 7 for x in the equation \sqrt{9x-28}=\sqrt{5x}.

$$\sqrt{9\times 7-28}=\sqrt{5\times 7}$$

Simplify. The value x=7 satisfies the equation.

$$35^{\frac{1}{2}}=35^{\frac{1}{2}}$$

Equation \sqrt{9x-28}=\sqrt{5x} has a unique solution.

$$x=7$$