Solve sqrt{6x+5}=sqrt{41-2x}

$$\sqrt { 6 x + 5 } = \sqrt { 41 - 2 x }$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{6x+5}\right)^{2}=\left(\sqrt{41-2x}\right)^{2}$$

Calculate \sqrt{6x+5} to the power of 2 and get 6x+5.

$$6x+5=\left(\sqrt{41-2x}\right)^{2}$$

Calculate \sqrt{41-2x} to the power of 2 and get 41-2x.

$$6x+5=41-2x$$

Add 2x to both sides.

$$6x+5+2x=41$$

Combine 6x and 2x to get 8x.

$$8x+5=41$$

Subtract 5 from both sides.

$$8x=41-5$$

Subtract 5 from 41 to get 36.

$$8x=36$$

Divide both sides by 8.

$$x=\frac{36}{8}$$

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{9}{2}$$

Substitute \frac{9}{2} for x in the equation \sqrt{6x+5}=\sqrt{41-2x}.

$$\sqrt{6\times \frac{9}{2}+5}=\sqrt{41-2\times \frac{9}{2}}$$

Simplify. The value x=\frac{9}{2} satisfies the equation.

$$4\times 2^{\frac{1}{2}}=4\times 2^{\frac{1}{2}}$$

Equation \sqrt{6x+5}=\sqrt{41-2x} has a unique solution.

$$x=\frac{9}{2}$$