Solve x5+5/526sqrt{2}(1.4/12)

$$x5+ \frac{ 5 }{ 526 \sqrt{ 2 } } ( \frac{ 1.4 }{ 12 } )$$

Evaluate

$$x_{5} = \frac{7 \sqrt{2}}{12624} = 0.0007841805241295679$$

Short Solution Steps

Rationalize the denominator of \frac{5}{526\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$x_{5}+\frac{5\sqrt{2}}{526\left(\sqrt{2}\right)^{2}}\times \frac{1.4}{12}$$

The square of \sqrt{2} is 2.

$$x_{5}+\frac{5\sqrt{2}}{526\times 2}\times \frac{1.4}{12}$$

Multiply 526 and 2 to get 1052.

$$x_{5}+\frac{5\sqrt{2}}{1052}\times \frac{1.4}{12}$$

Expand \frac{1.4}{12} by multiplying both numerator and the denominator by 10.

$$x_{5}+\frac{5\sqrt{2}}{1052}\times \frac{14}{120}$$

Reduce the fraction \frac{14}{120} to lowest terms by extracting and canceling out 2.

$$x_{5}+\frac{5\sqrt{2}}{1052}\times \frac{7}{60}$$

Multiply \frac{5\sqrt{2}}{1052} times \frac{7}{60} by multiplying numerator times numerator and denominator times denominator.

$$x_{5}+\frac{5\sqrt{2}\times 7}{1052\times 60}$$

Cancel out 5 in both numerator and denominator.

$$x_{5}+\frac{7\sqrt{2}}{12\times 1052}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x_{5} times \frac{12\times 1052}{12\times 1052}.

$$\frac{x_{5}\times 12\times 1052}{12\times 1052}+\frac{7\sqrt{2}}{12\times 1052}$$

Since \frac{x_{5}\times 12\times 1052}{12\times 1052} and \frac{7\sqrt{2}}{12\times 1052} have the same denominator, add them by adding their numerators.

$$\frac{x_{5}\times 12\times 1052+7\sqrt{2}}{12\times 1052}$$

Do the multiplications in x_{5}\times 12\times 1052+7\sqrt{2}.

$$\frac{12624x_{5}+7\sqrt{2}}{12\times 1052}$$

Expand 12\times 1052.

$$\frac{12624x_{5}+7\sqrt{2}}{12624}$$

Factor

$$\frac{12624x_{5}+7\sqrt{2}}{12624}$$