Solve sqrt{2x+15}=sqrt{5x+3}

$$\sqrt { 2 x + 15 } = \sqrt { 5 x + 3 }$$

Solve for x

$$x=4$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x+15}\right)^{2}=\left(\sqrt{5x+3}\right)^{2}$$

Calculate \sqrt{2x+15} to the power of 2 and get 2x+15.

$$2x+15=\left(\sqrt{5x+3}\right)^{2}$$

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

$$2x+15=5x+3$$

Subtract 5x from both sides.

$$2x+15-5x=3$$

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

$$-3x+15=3$$

Subtract 15 from both sides.

$$-3x=3-15$$

Subtract 15 from 3 to get -12.

$$-3x=-12$$

Divide both sides by -3.

$$x=\frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$x=4$$

Substitute 4 for x in the equation \sqrt{2x+15}=\sqrt{5x+3}.

$$\sqrt{2\times 4+15}=\sqrt{5\times 4+3}$$

Simplify. The value x=4 satisfies the equation.

$$23^{\frac{1}{2}}=23^{\frac{1}{2}}$$

Equation \sqrt{2x+15}=\sqrt{5x+3} has a unique solution.

$$x=4$$