Solve sqrt{9x-4}=sqrt{8x+1}

$$\sqrt { 9 x - 4 } = \sqrt { 8 x + 1 }$$

Solve for x

$$x=5$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{9x-4}\right)^{2}=\left(\sqrt{8x+1}\right)^{2}$$

Calculate \sqrt{9x-4} to the power of 2 and get 9x-4.

$$9x-4=\left(\sqrt{8x+1}\right)^{2}$$

Calculate \sqrt{8x+1} to the power of 2 and get 8x+1.

$$9x-4=8x+1$$

Subtract 8x from both sides.

$$9x-4-8x=1$$

Combine 9x and -8x to get x.

$$x-4=1$$

Add 4 to both sides.

$$x=1+4$$

Add 1 and 4 to get 5.

$$x=5$$

Substitute 5 for x in the equation \sqrt{9x-4}=\sqrt{8x+1}.

$$\sqrt{9\times 5-4}=\sqrt{8\times 5+1}$$

Simplify. The value x=5 satisfies the equation.

$$41^{\frac{1}{2}}=41^{\frac{1}{2}}$$

Equation \sqrt{9x-4}=\sqrt{8x+1} has a unique solution.

$$x=5$$