Solve 1.475(x/sqrt{15})=1422.1914

$$1.475( \frac{ x }{ \sqrt{ 15 } } )=1422.1914$$

Solve for x

$$x = \frac{7110957 \sqrt{15}}{7375} \approx 3734.321089708$$

Steps for Solving Linear Equation

Divide both sides by 1.475.

$$\frac{x}{\sqrt{15}}=\frac{1422.1914}{1.475}$$

Expand \frac{1422.1914}{1.475} by multiplying both numerator and the denominator by 10000.

$$\frac{x}{\sqrt{15}}=\frac{14221914}{14750}$$

Reduce the fraction \frac{14221914}{14750} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\sqrt{15}}=\frac{7110957}{7375}$$

Rationalize the denominator of \frac{x}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{x\sqrt{15}}{\left(\sqrt{15}\right)^{2}}=\frac{7110957}{7375}$$

The square of \sqrt{15} is 15.

$$\frac{x\sqrt{15}}{15}=\frac{7110957}{7375}$$

Multiply both sides by 15.

$$x\sqrt{15}=\frac{7110957}{7375}\times 15$$

Express \frac{7110957}{7375}\times 15 as a single fraction.

$$x\sqrt{15}=\frac{7110957\times 15}{7375}$$

Multiply 7110957 and 15 to get 106664355.

$$x\sqrt{15}=\frac{106664355}{7375}$$

Reduce the fraction \frac{106664355}{7375} to lowest terms by extracting and canceling out 5.

$$x\sqrt{15}=\frac{21332871}{1475}$$

The equation is in standard form.

$$\sqrt{15}x=\frac{21332871}{1475}$$

Divide both sides by \sqrt{15}.

$$\frac{\sqrt{15}x}{\sqrt{15}}=\frac{\frac{21332871}{1475}}{\sqrt{15}}$$

Dividing by \sqrt{15} undoes the multiplication by \sqrt{15}.

$$x=\frac{\frac{21332871}{1475}}{\sqrt{15}}$$

Divide \frac{21332871}{1475} by \sqrt{15}.

$$x=\frac{7110957\sqrt{15}}{7375}$$