Solve {l}{z=0.5-0.5412/sqrt{.525*0.475(frac{1{400}+1/600)}}}{Rightarrow}hline

$$\left. \begin{array} { l } { z = \frac { 0.5 - 0.5412 } { \sqrt { .525 \times 0.475 ( \frac { 1 } { 400 } + \frac { 1 } { 600 } ) } } } \\ { \Rightarrow } \\ \hline \end{array} \right.$$

Solve for z

$$z = -\frac{824 \sqrt{665}}{16625} \approx -1.278133978$$

Steps for Solving Linear Equation

Subtract 0.5412 from 0.5 to get -0.0412.

$$z=\frac{-0.0412}{\sqrt{0.525\times 0.475\left(\frac{1}{400}+\frac{1}{600}\right)}}$$

Multiply 0.525 and 0.475 to get 0.249375.

$$z=\frac{-0.0412}{\sqrt{0.249375\left(\frac{1}{400}+\frac{1}{600}\right)}}$$

Least common multiple of 400 and 600 is 1200. Convert \frac{1}{400} and \frac{1}{600} to fractions with denominator 1200.

$$z=\frac{-0.0412}{\sqrt{0.249375\left(\frac{3}{1200}+\frac{2}{1200}\right)}}$$

Since \frac{3}{1200} and \frac{2}{1200} have the same denominator, add them by adding their numerators.

$$z=\frac{-0.0412}{\sqrt{0.249375\times \frac{3+2}{1200}}}$$

Add 3 and 2 to get 5.

$$z=\frac{-0.0412}{\sqrt{0.249375\times \frac{5}{1200}}}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$z=\frac{-0.0412}{\sqrt{0.249375\times \frac{1}{240}}}$$

Convert decimal number 0.249375 to fraction \frac{249375}{1000000}. Reduce the fraction \frac{249375}{1000000} to lowest terms by extracting and canceling out 625.

$$z=\frac{-0.0412}{\sqrt{\frac{399}{1600}\times \frac{1}{240}}}$$

Multiply \frac{399}{1600} times \frac{1}{240} by multiplying numerator times numerator and denominator times denominator.

$$z=\frac{-0.0412}{\sqrt{\frac{399\times 1}{1600\times 240}}}$$

Do the multiplications in the fraction \frac{399\times 1}{1600\times 240}.

$$z=\frac{-0.0412}{\sqrt{\frac{399}{384000}}}$$

Reduce the fraction \frac{399}{384000} to lowest terms by extracting and canceling out 3.

$$z=\frac{-0.0412}{\sqrt{\frac{133}{128000}}}$$

Rewrite the square root of the division \sqrt{\frac{133}{128000}} as the division of square roots \frac{\sqrt{133}}{\sqrt{128000}}.

$$z=\frac{-0.0412}{\frac{\sqrt{133}}{\sqrt{128000}}}$$

Factor 128000=160^{2}\times 5. Rewrite the square root of the product \sqrt{160^{2}\times 5} as the product of square roots \sqrt{160^{2}}\sqrt{5}. Take the square root of 160^{2}.

$$z=\frac{-0.0412}{\frac{\sqrt{133}}{160\sqrt{5}}}$$

Rationalize the denominator of \frac{\sqrt{133}}{160\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$z=\frac{-0.0412}{\frac{\sqrt{133}\sqrt{5}}{160\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$z=\frac{-0.0412}{\frac{\sqrt{133}\sqrt{5}}{160\times 5}}$$

To multiply \sqrt{133} and \sqrt{5}, multiply the numbers under the square root.

$$z=\frac{-0.0412}{\frac{\sqrt{665}}{160\times 5}}$$

Multiply 160 and 5 to get 800.

$$z=\frac{-0.0412}{\frac{\sqrt{665}}{800}}$$

Divide -0.0412 by \frac{\sqrt{665}}{800} by multiplying -0.0412 by the reciprocal of \frac{\sqrt{665}}{800}.

$$z=\frac{-0.0412\times 800}{\sqrt{665}}$$

Rationalize the denominator of \frac{-0.0412\times 800}{\sqrt{665}} by multiplying numerator and denominator by \sqrt{665}.

$$z=\frac{-0.0412\times 800\sqrt{665}}{\left(\sqrt{665}\right)^{2}}$$

The square of \sqrt{665} is 665.

$$z=\frac{-0.0412\times 800\sqrt{665}}{665}$$

Multiply -0.0412 and 800 to get -32.96.

$$z=\frac{-32.96\sqrt{665}}{665}$$

Divide -32.96\sqrt{665} by 665 to get -\frac{824}{16625}\sqrt{665}.

$$z=-\frac{824}{16625}\sqrt{665}$$