Solve 2x+3=0+sqrt{5/53}

$$2x+3=0+ \sqrt{ \frac{ 5 }{ 53 } }$$

Solve for x

$$x=\frac{\sqrt{265}-159}{106}\approx -1.346426221$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{5}{53}} as the division of square roots \frac{\sqrt{5}}{\sqrt{53}}.

$$2x+3=0+\frac{\sqrt{5}}{\sqrt{53}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{53}} by multiplying numerator and denominator by \sqrt{53}.

$$2x+3=0+\frac{\sqrt{5}\sqrt{53}}{\left(\sqrt{53}\right)^{2}}$$

The square of \sqrt{53} is 53.

$$2x+3=0+\frac{\sqrt{5}\sqrt{53}}{53}$$

To multiply \sqrt{5} and \sqrt{53}, multiply the numbers under the square root.

$$2x+3=0+\frac{\sqrt{265}}{53}$$

Anything plus zero gives itself.

$$2x+3=\frac{\sqrt{265}}{53}$$

Subtract 3 from both sides.

$$2x=\frac{\sqrt{265}}{53}-3$$

Multiply both sides of the equation by 53.

$$106x=\sqrt{265}-159$$

Divide both sides by 106.

$$\frac{106x}{106}=\frac{\sqrt{265}-159}{106}$$

Dividing by 106 undoes the multiplication by 106.

$$x=\frac{\sqrt{265}-159}{106}$$

Divide \sqrt{265}-159 by 106.

$$x=\frac{\sqrt{265}}{106}-\frac{3}{2}$$