Solve sqrt{4x}=sqrt{5x-7}

$$\sqrt { 4 x } = \sqrt { 5 x - 7 }$$

Solve for x

$$x=7$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4x}\right)^{2}=\left(\sqrt{5x-7}\right)^{2}$$

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

$$4x=\left(\sqrt{5x-7}\right)^{2}$$

Calculate \sqrt{5x-7} to the power of 2 and get 5x-7.

$$4x=5x-7$$

Subtract 5x from both sides.

$$4x-5x=-7$$

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

$$-x=-7$$

Multiply both sides by -1.

$$x=7$$

Substitute 7 for x in the equation \sqrt{4x}=\sqrt{5x-7}.

$$\sqrt{4\times 7}=\sqrt{5\times 7-7}$$

Simplify. The value x=7 satisfies the equation.

$$2\times 7^{\frac{1}{2}}=2\times 7^{\frac{1}{2}}$$

Equation \sqrt{4x}=\sqrt{5x-7} has a unique solution.

$$x=7$$