Solve -0.55=25-25.6/frac{sigma{sqrt{42}}}

$$- 0.55 = \frac { 25 - 25.6 } { \frac { \sigma } { \sqrt { 42 } } }$$

Solve for σ

$$\sigma =\frac{12\sqrt{42}}{11}\approx 7.069898944$$

Steps for Solving Linear Equation

Subtract 25.6 from 25 to get -0.6.

$$-0.55=\frac{-0.6}{\frac{\sigma }{\sqrt{42}}}$$

Rationalize the denominator of \frac{\sigma }{\sqrt{42}} by multiplying numerator and denominator by \sqrt{42}.

$$-0.55=\frac{-0.6}{\frac{\sigma \sqrt{42}}{\left(\sqrt{42}\right)^{2}}}$$

The square of \sqrt{42} is 42.

$$-0.55=\frac{-0.6}{\frac{\sigma \sqrt{42}}{42}}$$

Divide -0.6 by \frac{\sigma \sqrt{42}}{42} by multiplying -0.6 by the reciprocal of \frac{\sigma \sqrt{42}}{42}.

$$-0.55=\frac{-0.6\times 42}{\sigma \sqrt{42}}$$

Factor the expressions that are not already factored in \frac{-0.6\times 42}{\sigma \sqrt{42}}.

$$-0.55=\frac{-0.6\times 42}{\sqrt{42}\sigma }$$

Cancel out \sqrt{42} in both numerator and denominator.

$$-0.55=\frac{-0.6\sqrt{42}}{\sigma }$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{-0.6\sqrt{42}}{\sigma }=-0.55$$

Variable \sigma cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \sigma .

$$-0.6\sqrt{42}=-0.55\sigma$$

Swap sides so that all variable terms are on the left hand side.

$$-0.55\sigma =-0.6\sqrt{42}$$

The equation is in standard form.

$$-0.55\sigma =-\frac{3\sqrt{42}}{5}$$

Divide both sides of the equation by -0.55, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.55\sigma }{-0.55}=-\frac{\frac{3\sqrt{42}}{5}}{-0.55}$$

Dividing by -0.55 undoes the multiplication by -0.55.

$$\sigma =-\frac{\frac{3\sqrt{42}}{5}}{-0.55}$$

Divide -\frac{3\sqrt{42}}{5} by -0.55 by multiplying -\frac{3\sqrt{42}}{5} by the reciprocal of -0.55.

$$\sigma =\frac{12\sqrt{42}}{11}$$