Solve t=(0.78894-0.80234)-0/sqrt{frac{0.004411^2{35}+0.00744^2/35}}

$$t = \frac { ( 0.78894 - 0.80234 ) - 0 } { \sqrt { \frac { 0.004411 ^ { 2 } } { 35 } + \frac { 0.00744 ^ { 2 } } { 35 } } }$$

Solve for t

$$t = -\frac{13400 \sqrt{2618368235}}{74810521} \approx -9.16552784$$

Steps for Solving Linear Equation

Subtract 0.80234 from 0.78894 to get -0.0134.

$$t=\frac{-0.0134-0}{\sqrt{\frac{0.004411^{2}}{35}+\frac{0.00744^{2}}{35}}}$$

Subtract 0 from -0.0134 to get -0.0134.

$$t=\frac{-0.0134}{\sqrt{\frac{0.004411^{2}}{35}+\frac{0.00744^{2}}{35}}}$$

Calculate 0.004411 to the power of 2 and get 0.000019456921.

$$t=\frac{-0.0134}{\sqrt{\frac{0.000019456921}{35}+\frac{0.00744^{2}}{35}}}$$

Expand \frac{0.000019456921}{35} by multiplying both numerator and the denominator by 1000000000000.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921}{35000000000000}+\frac{0.00744^{2}}{35}}}$$

Calculate 0.00744 to the power of 2 and get 0.0000553536.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921}{35000000000000}+\frac{0.0000553536}{35}}}$$

Expand \frac{0.0000553536}{35} by multiplying both numerator and the denominator by 10000000000.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921}{35000000000000}+\frac{553536}{350000000000}}}$$

Reduce the fraction \frac{553536}{350000000000} to lowest terms by extracting and canceling out 64.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921}{35000000000000}+\frac{8649}{5468750000}}}$$

Least common multiple of 35000000000000 and 5468750000 is 35000000000000. Convert \frac{19456921}{35000000000000} and \frac{8649}{5468750000} to fractions with denominator 35000000000000.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921}{35000000000000}+\frac{55353600}{35000000000000}}}$$

Since \frac{19456921}{35000000000000} and \frac{55353600}{35000000000000} have the same denominator, add them by adding their numerators.

$$t=\frac{-0.0134}{\sqrt{\frac{19456921+55353600}{35000000000000}}}$$

Add 19456921 and 55353600 to get 74810521.

$$t=\frac{-0.0134}{\sqrt{\frac{74810521}{35000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{74810521}{35000000000000}} as the division of square roots \frac{\sqrt{74810521}}{\sqrt{35000000000000}}.

$$t=\frac{-0.0134}{\frac{\sqrt{74810521}}{\sqrt{35000000000000}}}$$

Factor 35000000000000=1000000^{2}\times 35. Rewrite the square root of the product \sqrt{1000000^{2}\times 35} as the product of square roots \sqrt{1000000^{2}}\sqrt{35}. Take the square root of 1000000^{2}.

$$t=\frac{-0.0134}{\frac{\sqrt{74810521}}{1000000\sqrt{35}}}$$

Rationalize the denominator of \frac{\sqrt{74810521}}{1000000\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$t=\frac{-0.0134}{\frac{\sqrt{74810521}\sqrt{35}}{1000000\left(\sqrt{35}\right)^{2}}}$$

The square of \sqrt{35} is 35.

$$t=\frac{-0.0134}{\frac{\sqrt{74810521}\sqrt{35}}{1000000\times 35}}$$

To multiply \sqrt{74810521} and \sqrt{35}, multiply the numbers under the square root.

$$t=\frac{-0.0134}{\frac{\sqrt{2618368235}}{1000000\times 35}}$$

Multiply 1000000 and 35 to get 35000000.

$$t=\frac{-0.0134}{\frac{\sqrt{2618368235}}{35000000}}$$

Divide -0.0134 by \frac{\sqrt{2618368235}}{35000000} by multiplying -0.0134 by the reciprocal of \frac{\sqrt{2618368235}}{35000000}.

$$t=\frac{-0.0134\times 35000000}{\sqrt{2618368235}}$$

Rationalize the denominator of \frac{-0.0134\times 35000000}{\sqrt{2618368235}} by multiplying numerator and denominator by \sqrt{2618368235}.

$$t=\frac{-0.0134\times 35000000\sqrt{2618368235}}{\left(\sqrt{2618368235}\right)^{2}}$$

The square of \sqrt{2618368235} is 2618368235.

$$t=\frac{-0.0134\times 35000000\sqrt{2618368235}}{2618368235}$$

Multiply -0.0134 and 35000000 to get -469000.

$$t=\frac{-469000\sqrt{2618368235}}{2618368235}$$

Divide -469000\sqrt{2618368235} by 2618368235 to get -\frac{13400}{74810521}\sqrt{2618368235}.

$$t=-\frac{13400}{74810521}\sqrt{2618368235}$$

Assign t

$$t≔-\frac{13400\sqrt{2618368235}}{74810521}$$