Solve 75+x(1.58/sqrt{35})=75.523

$$75+x( \frac{ 1.58 }{ \sqrt{ 35 } } )=75.523$$

Solve for x

$$x = \frac{523 \sqrt{35}}{1580} \approx 1.958297295$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1.58}{\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$75+x\times \frac{1.58\sqrt{35}}{\left(\sqrt{35}\right)^{2}}=75.523$$

The square of \sqrt{35} is 35.

$$75+x\times \frac{1.58\sqrt{35}}{35}=75.523$$

Divide 1.58\sqrt{35} by 35 to get \frac{79}{1750}\sqrt{35}.

$$75+x\times \frac{79}{1750}\sqrt{35}=75.523$$

Subtract 75 from both sides.

$$x\times \frac{79}{1750}\sqrt{35}=75.523-75$$

Subtract 75 from 75.523 to get 0.523.

$$x\times \frac{79}{1750}\sqrt{35}=0.523$$

The equation is in standard form.

$$\frac{79\sqrt{35}}{1750}x=0.523$$

Divide both sides by \frac{79}{1750}\sqrt{35}.

$$\frac{1750\times \frac{79\sqrt{35}}{1750}x}{79\sqrt{35}}=\frac{0.523\times 1750}{79\sqrt{35}}$$

Dividing by \frac{79}{1750}\sqrt{35} undoes the multiplication by \frac{79}{1750}\sqrt{35}.

$$x=\frac{0.523\times 1750}{79\sqrt{35}}$$

Divide 0.523 by \frac{79}{1750}\sqrt{35}.

$$x=\frac{523\sqrt{35}}{1580}$$