Solve 5/28sqrt{50x+100}=20sqrt{5}

$$\frac { 5 } { 28 } \sqrt { 50 x + 100 } = 20 \sqrt { 5 }$$

Solve for x

$$x = \frac{6262}{5} = 1252\frac{2}{5} = 1252.4$$

Steps for Solving Radical Equations

Divide both sides of the equation by \frac{5}{28}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{28}\sqrt{50x+100}}{\frac{5}{28}}=\frac{20\sqrt{5}}{\frac{5}{28}}$$

Dividing by \frac{5}{28} undoes the multiplication by \frac{5}{28}.

$$\sqrt{50x+100}=\frac{20\sqrt{5}}{\frac{5}{28}}$$

Divide 20\sqrt{5} by \frac{5}{28} by multiplying 20\sqrt{5} by the reciprocal of \frac{5}{28}.

$$\sqrt{50x+100}=112\sqrt{5}$$

Square both sides of the equation.

$$50x+100=62720$$

Subtract 100 from both sides of the equation.

$$50x+100-100=62720-100$$

Subtracting 100 from itself leaves 0.

$$50x=62720-100$$

Subtract 100 from 62720.

$$50x=62620$$

Divide both sides by 50.

$$\frac{50x}{50}=\frac{62620}{50}$$

Dividing by 50 undoes the multiplication by 50.

$$x=\frac{62620}{50}$$

Reduce the fraction \frac{62620}{50} to lowest terms by extracting and canceling out 10.

$$x=\frac{6262}{5}$$