Solve sqrt{5/52}+3x-3=0

$$\sqrt{ \frac{ 5 }{ 52 } } +3x-3=0$$

Solve for x

$$x=-\frac{\sqrt{65}}{78}+1\approx 0.896637721$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{5}{52}} as the division of square roots \frac{\sqrt{5}}{\sqrt{52}}.

$$\frac{\sqrt{5}}{\sqrt{52}}+3x-3=0$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{\sqrt{5}}{2\sqrt{13}}+3x-3=0$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{5}\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}+3x-3=0$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{5}\sqrt{13}}{2\times 13}+3x-3=0$$

To multiply \sqrt{5} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\sqrt{65}}{2\times 13}+3x-3=0$$

Multiply 2 and 13 to get 26.

$$\frac{\sqrt{65}}{26}+3x-3=0$$

Subtract \frac{\sqrt{65}}{26} from both sides. Anything subtracted from zero gives its negation.

$$3x-3=-\frac{\sqrt{65}}{26}$$

Add 3 to both sides.

$$3x=-\frac{\sqrt{65}}{26}+3$$

Multiply both sides of the equation by 26.

$$78x=-\sqrt{65}+78$$

The equation is in standard form.

$$78x=78-\sqrt{65}$$

Divide both sides by 78.

$$\frac{78x}{78}=\frac{78-\sqrt{65}}{78}$$

Dividing by 78 undoes the multiplication by 78.

$$x=\frac{78-\sqrt{65}}{78}$$

Divide -\sqrt{65}+78 by 78.

$$x=-\frac{\sqrt{65}}{78}+1$$