Solve sqrt{3x+4}=sqrt{2x+5}

$$\sqrt{ 3x+4 } = \sqrt{ 2x+5 }$$

Solve for x

$$x=1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3x+4}\right)^{2}=\left(\sqrt{2x+5}\right)^{2}$$

Calculate \sqrt{3x+4} to the power of 2 and get 3x+4.

$$3x+4=\left(\sqrt{2x+5}\right)^{2}$$

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

$$3x+4=2x+5$$

Subtract 2x from both sides.

$$3x+4-2x=5$$

Combine 3x and -2x to get x.

$$x+4=5$$

Subtract 4 from both sides.

$$x=5-4$$

Subtract 4 from 5 to get 1.

$$x=1$$

Substitute 1 for x in the equation \sqrt{3x+4}=\sqrt{2x+5}.

$$\sqrt{3\times 1+4}=\sqrt{2\times 1+5}$$

Simplify. The value x=1 satisfies the equation.

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

Equation \sqrt{3x+4}=\sqrt{2x+5} has a unique solution.

$$x=1$$