Solve sqrt{5x-3}=sqrt{2x+3}

$$\sqrt { 5 x - 3 } = \sqrt { 2 x + 3 }$$

Solve for x

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5x-3}\right)^{2}=\left(\sqrt{2x+3}\right)^{2}$$

Calculate \sqrt{5x-3} to the power of 2 and get 5x-3.

$$5x-3=\left(\sqrt{2x+3}\right)^{2}$$

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

$$5x-3=2x+3$$

Subtract 2x from both sides.

$$5x-3-2x=3$$

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

$$3x-3=3$$

Add 3 to both sides.

$$3x=3+3$$

Add 3 and 3 to get 6.

$$3x=6$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

Substitute 2 for x in the equation \sqrt{5x-3}=\sqrt{2x+3}.

$$\sqrt{5\times 2-3}=\sqrt{2\times 2+3}$$

Simplify. The value x=2 satisfies the equation.

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

Equation \sqrt{5x-3}=\sqrt{2x+3} has a unique solution.

$$x=2$$