Solve 100.862-0.0415sqrt{h+431.03}=98

$$100.862-0.0415 \sqrt{ h+431.03 } = 98$$

Solve for h

$$h = \frac{2979481033}{688900} = 4324\frac{677433}{688900} \approx 4324.983354623$$

Steps for Solving Radical Equations

Subtract 100.862 from both sides of the equation.

$$-0.0415\sqrt{h+431.03}+100.862-100.862=98-100.862$$

Subtracting 100.862 from itself leaves 0.

$$-0.0415\sqrt{h+431.03}=98-100.862$$

Subtract 100.862 from 98.

$$-0.0415\sqrt{h+431.03}=-2.862$$

Divide both sides of the equation by -0.0415, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.0415\sqrt{h+431.03}}{-0.0415}=-\frac{2.862}{-0.0415}$$

Dividing by -0.0415 undoes the multiplication by -0.0415.

$$\sqrt{h+431.03}=-\frac{2.862}{-0.0415}$$

Divide -2.862 by -0.0415 by multiplying -2.862 by the reciprocal of -0.0415.

$$\sqrt{h+431.03}=\frac{5724}{83}$$

Square both sides of the equation.

$$h+431.03=\frac{32764176}{6889}$$

Subtract 431.03 from both sides of the equation.

$$h+431.03-431.03=\frac{32764176}{6889}-431.03$$

Subtracting 431.03 from itself leaves 0.

$$h=\frac{32764176}{6889}-431.03$$

Subtract 431.03 from \frac{32764176}{6889} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$h=\frac{2979481033}{688900}$$