Solve 26x=sqrt{9x^2/8}

$$26x= \sqrt{ \frac{ 9 { x }^{ 2 } }{ 8 } }$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(26x\right)^{2}=\left(\sqrt{\frac{9x^{2}}{8}}\right)^{2}$$

Expand \left(26x\right)^{2}.

$$26^{2}x^{2}=\left(\sqrt{\frac{9x^{2}}{8}}\right)^{2}$$

Calculate 26 to the power of 2 and get 676.

$$676x^{2}=\left(\sqrt{\frac{9x^{2}}{8}}\right)^{2}$$

Calculate \sqrt{\frac{9x^{2}}{8}} to the power of 2 and get \frac{9x^{2}}{8}.

$$676x^{2}=\frac{9x^{2}}{8}$$

Multiply both sides of the equation by 8.

$$5408x^{2}=9x^{2}$$

Subtract 9x^{2} from both sides.

$$5408x^{2}-9x^{2}=0$$

Combine 5408x^{2} and -9x^{2} to get 5399x^{2}.

$$5399x^{2}=0$$

Divide both sides by 5399. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Substitute 0 for x in the equation 26x=\sqrt{\frac{9x^{2}}{8}}.

$$26\times 0=\sqrt{\frac{9\times 0^{2}}{8}}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation 26x=\sqrt{\frac{9x^{2}}{8}} has a unique solution.

$$x=0$$