Solve operatorname{ars}=(75.09-80.60)/sqrt{(frac{144^2{21})+(1.63^2/21)}}

$$\operatorname { ars } = \frac { ( 75.09 - 80.60 ) } { \sqrt { ( \frac { 144 ^ { 2 } } { 21 } ) + ( \frac { 1.63 ^ { 2 } } { 21 } ) } }$$

Solve for a

$$a=-\frac{19\sqrt{4355117949}}{7151261rs}$$

$$s\neq 0\text{ and }r\neq 0$$

Steps for Solving Linear Equation

Subtract 80.6 from 75.09 to get -5.51.

$$ars=\frac{-5.51}{\sqrt{\frac{144^{2}}{21}+\frac{1.63^{2}}{21}}}$$

Calculate 144 to the power of 2 and get 20736.

$$ars=\frac{-5.51}{\sqrt{\frac{20736}{21}+\frac{1.63^{2}}{21}}}$$

Reduce the fraction \frac{20736}{21} to lowest terms by extracting and canceling out 3.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{1.63^{2}}{21}}}$$

Calculate 1.63 to the power of 2 and get 2.6569.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{2.6569}{21}}}$$

Expand \frac{2.6569}{21} by multiplying both numerator and the denominator by 10000.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{26569}{210000}}}$$

Add \frac{6912}{7} and \frac{26569}{210000} to get \frac{207386569}{210000}.

$$ars=\frac{-5.51}{\sqrt{\frac{207386569}{210000}}}$$

Rewrite the square root of the division \sqrt{\frac{207386569}{210000}} as the division of square roots \frac{\sqrt{207386569}}{\sqrt{210000}}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}}{\sqrt{210000}}}$$

Factor 210000=100^{2}\times 21. Rewrite the square root of the product \sqrt{100^{2}\times 21} as the product of square roots \sqrt{100^{2}}\sqrt{21}. Take the square root of 100^{2}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}}{100\sqrt{21}}}$$

Rationalize the denominator of \frac{\sqrt{207386569}}{100\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}\sqrt{21}}{100\left(\sqrt{21}\right)^{2}}}$$

The square of \sqrt{21} is 21.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}\sqrt{21}}{100\times 21}}$$

To multiply \sqrt{207386569} and \sqrt{21}, multiply the numbers under the square root.

$$ars=\frac{-5.51}{\frac{\sqrt{4355117949}}{100\times 21}}$$

Multiply 100 and 21 to get 2100.

$$ars=\frac{-5.51}{\frac{\sqrt{4355117949}}{2100}}$$

Divide -5.51 by \frac{\sqrt{4355117949}}{2100} by multiplying -5.51 by the reciprocal of \frac{\sqrt{4355117949}}{2100}.

$$ars=\frac{-5.51\times 2100}{\sqrt{4355117949}}$$

Rationalize the denominator of \frac{-5.51\times 2100}{\sqrt{4355117949}} by multiplying numerator and denominator by \sqrt{4355117949}.

$$ars=\frac{-5.51\times 2100\sqrt{4355117949}}{\left(\sqrt{4355117949}\right)^{2}}$$

The square of \sqrt{4355117949} is 4355117949.

$$ars=\frac{-5.51\times 2100\sqrt{4355117949}}{4355117949}$$

Multiply -5.51 and 2100 to get -11571.

$$ars=\frac{-11571\sqrt{4355117949}}{4355117949}$$

Divide -11571\sqrt{4355117949} by 4355117949 to get -\frac{19}{7151261}\sqrt{4355117949}.

$$ars=-\frac{19}{7151261}\sqrt{4355117949}$$

The equation is in standard form.

$$rsa=-\frac{19\sqrt{4355117949}}{7151261}$$

Divide both sides by rs.

$$\frac{rsa}{rs}=-\frac{\frac{19\sqrt{4355117949}}{7151261}}{rs}$$

Dividing by rs undoes the multiplication by rs.

$$a=-\frac{\frac{19\sqrt{4355117949}}{7151261}}{rs}$$

Divide -\frac{19\sqrt{4355117949}}{7151261} by rs.

$$a=-\frac{19\sqrt{4355117949}}{7151261rs}$$

Solve for r

$$r=-\frac{19\sqrt{4355117949}}{7151261as}$$

$$s\neq 0\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Subtract 80.6 from 75.09 to get -5.51.

$$ars=\frac{-5.51}{\sqrt{\frac{144^{2}}{21}+\frac{1.63^{2}}{21}}}$$

Calculate 144 to the power of 2 and get 20736.

$$ars=\frac{-5.51}{\sqrt{\frac{20736}{21}+\frac{1.63^{2}}{21}}}$$

Reduce the fraction \frac{20736}{21} to lowest terms by extracting and canceling out 3.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{1.63^{2}}{21}}}$$

Calculate 1.63 to the power of 2 and get 2.6569.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{2.6569}{21}}}$$

Expand \frac{2.6569}{21} by multiplying both numerator and the denominator by 10000.

$$ars=\frac{-5.51}{\sqrt{\frac{6912}{7}+\frac{26569}{210000}}}$$

Add \frac{6912}{7} and \frac{26569}{210000} to get \frac{207386569}{210000}.

$$ars=\frac{-5.51}{\sqrt{\frac{207386569}{210000}}}$$

Rewrite the square root of the division \sqrt{\frac{207386569}{210000}} as the division of square roots \frac{\sqrt{207386569}}{\sqrt{210000}}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}}{\sqrt{210000}}}$$

Factor 210000=100^{2}\times 21. Rewrite the square root of the product \sqrt{100^{2}\times 21} as the product of square roots \sqrt{100^{2}}\sqrt{21}. Take the square root of 100^{2}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}}{100\sqrt{21}}}$$

Rationalize the denominator of \frac{\sqrt{207386569}}{100\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}\sqrt{21}}{100\left(\sqrt{21}\right)^{2}}}$$

The square of \sqrt{21} is 21.

$$ars=\frac{-5.51}{\frac{\sqrt{207386569}\sqrt{21}}{100\times 21}}$$

To multiply \sqrt{207386569} and \sqrt{21}, multiply the numbers under the square root.

$$ars=\frac{-5.51}{\frac{\sqrt{4355117949}}{100\times 21}}$$

Multiply 100 and 21 to get 2100.

$$ars=\frac{-5.51}{\frac{\sqrt{4355117949}}{2100}}$$

Divide -5.51 by \frac{\sqrt{4355117949}}{2100} by multiplying -5.51 by the reciprocal of \frac{\sqrt{4355117949}}{2100}.

$$ars=\frac{-5.51\times 2100}{\sqrt{4355117949}}$$

Rationalize the denominator of \frac{-5.51\times 2100}{\sqrt{4355117949}} by multiplying numerator and denominator by \sqrt{4355117949}.

$$ars=\frac{-5.51\times 2100\sqrt{4355117949}}{\left(\sqrt{4355117949}\right)^{2}}$$

The square of \sqrt{4355117949} is 4355117949.

$$ars=\frac{-5.51\times 2100\sqrt{4355117949}}{4355117949}$$

Multiply -5.51 and 2100 to get -11571.

$$ars=\frac{-11571\sqrt{4355117949}}{4355117949}$$

Divide -11571\sqrt{4355117949} by 4355117949 to get -\frac{19}{7151261}\sqrt{4355117949}.

$$ars=-\frac{19}{7151261}\sqrt{4355117949}$$

The equation is in standard form.

$$asr=-\frac{19\sqrt{4355117949}}{7151261}$$

Divide both sides by as.

$$\frac{asr}{as}=-\frac{\frac{19\sqrt{4355117949}}{7151261}}{as}$$

Dividing by as undoes the multiplication by as.

$$r=-\frac{\frac{19\sqrt{4355117949}}{7151261}}{as}$$

Divide -\frac{19\sqrt{4355117949}}{7151261} by as.

$$r=-\frac{19\sqrt{4355117949}}{7151261as}$$