Solve (h-17.6*2)*9.81=1/2*(13.14)^2

$$( h - 17.6 \times 2 ) \cdot 9.81 = \frac { 1 } { 2 } \cdot ( 13.14 ) ^ { 2 }$$

Solve for h

$$h = \frac{239801}{5450} = 44\frac{1}{5450} \approx 44.000183486$$

Steps for Solving Linear Equation

Multiply 17.6 and 2 to get 35.2.

$$\left(h-35.2\right)\times 9.81=\frac{1}{2}\times 13.14^{2}$$

Use the distributive property to multiply h-35.2 by 9.81.

$$9.81h-345.312=\frac{1}{2}\times 13.14^{2}$$

Calculate 13.14 to the power of 2 and get 172.6596.

$$9.81h-345.312=\frac{1}{2}\times 172.6596$$

Convert decimal number 172.6596 to fraction \frac{1726596}{10000}. Reduce the fraction \frac{1726596}{10000} to lowest terms by extracting and canceling out 4.

$$9.81h-345.312=\frac{1}{2}\times \frac{431649}{2500}$$

Multiply \frac{1}{2} times \frac{431649}{2500} by multiplying numerator times numerator and denominator times denominator.

$$9.81h-345.312=\frac{1\times 431649}{2\times 2500}$$

Do the multiplications in the fraction \frac{1\times 431649}{2\times 2500}.

$$9.81h-345.312=\frac{431649}{5000}$$

Add 345.312 to both sides.

$$9.81h=\frac{431649}{5000}+345.312$$

Convert decimal number 345.312 to fraction \frac{345312}{1000}. Reduce the fraction \frac{345312}{1000} to lowest terms by extracting and canceling out 8.

$$9.81h=\frac{431649}{5000}+\frac{43164}{125}$$

Least common multiple of 5000 and 125 is 5000. Convert \frac{431649}{5000} and \frac{43164}{125} to fractions with denominator 5000.

$$9.81h=\frac{431649}{5000}+\frac{1726560}{5000}$$

Since \frac{431649}{5000} and \frac{1726560}{5000} have the same denominator, add them by adding their numerators.

$$9.81h=\frac{431649+1726560}{5000}$$

Add 431649 and 1726560 to get 2158209.

$$9.81h=\frac{2158209}{5000}$$

Divide both sides by 9.81.

$$h=\frac{\frac{2158209}{5000}}{9.81}$$

Express \frac{\frac{2158209}{5000}}{9.81} as a single fraction.

$$h=\frac{2158209}{5000\times 9.81}$$

Multiply 5000 and 9.81 to get 49050.

$$h=\frac{2158209}{49050}$$

Reduce the fraction \frac{2158209}{49050} to lowest terms by extracting and canceling out 9.

$$h=\frac{239801}{5450}$$