Solve 2.8(5/26sin35^circ)-0.7(252)-1.4(5)=0

$$2.8 ( 5 / 26 \sin 35 ^ { \circ } ) - 0.7 ( 252 ) - 1.4 ( 5 ) = 0$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$2.8 {(\frac{5}{26} 0.573576436351046)} - 0.7 {(252)} - 1.4 {(5)} = 0$$

Convert decimal number 2.8 to fraction \frac{28}{10}. Reduce the fraction \frac{28}{10} to lowest terms by extracting and canceling out 2.

$$\frac{14}{5}\times \frac{5}{26}\times 0.573576436351046-0.7\times 252-1.4\times 5=0$$

Multiply \frac{14}{5} times \frac{5}{26} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 5}{5\times 26}\times 0.573576436351046-0.7\times 252-1.4\times 5=0$$

Cancel out 5 in both numerator and denominator.

$$\frac{14}{26}\times 0.573576436351046-0.7\times 252-1.4\times 5=0$$

Reduce the fraction \frac{14}{26} to lowest terms by extracting and canceling out 2.

$$\frac{7}{13}\times 0.573576436351046-0.7\times 252-1.4\times 5=0$$

Convert decimal number 0.573576436351046 to fraction \frac{286788218175523}{10000000000}. Reduce the fraction \frac{286788218175523}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{7}{13}\times \frac{286788218175523}{500000000000000}-0.7\times 252-1.4\times 5=0$$

Multiply \frac{7}{13} times \frac{286788218175523}{500000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 286788218175523}{13\times 500000000000000}-0.7\times 252-1.4\times 5=0$$

Do the multiplications in the fraction \frac{7\times 286788218175523}{13\times 500000000000000}.

$$\frac{2007517527228661}{6500000000000000}-0.7\times 252-1.4\times 5=0$$

Multiply 0.7 and 252 to get 176.4.

$$\frac{2007517527228661}{6500000000000000}-176.4-1.4\times 5=0$$

Convert decimal number 176.4 to fraction \frac{1764}{10}. Reduce the fraction \frac{1764}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2007517527228661}{6500000000000000}-\frac{882}{5}-1.4\times 5=0$$

Least common multiple of 6500000000000000 and 5 is 6500000000000000. Convert \frac{2007517527228661}{6500000000000000} and \frac{882}{5} to fractions with denominator 6500000000000000.

$$\frac{2007517527228661}{6500000000000000}-\frac{1146600000000000000}{6500000000000000}-1.4\times 5=0$$

Since \frac{2007517527228661}{6500000000000000} and \frac{1146600000000000000}{6500000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2007517527228661-1146600000000000000}{6500000000000000}-1.4\times 5=0$$

Subtract 1146600000000000000 from 2007517527228661 to get -1144592482472771339.

$$-\frac{1144592482472771339}{6500000000000000}-1.4\times 5=0$$

Multiply 1.4 and 5 to get 7.

$$-\frac{1144592482472771339}{6500000000000000}-7=0$$

Convert 7 to fraction \frac{45500000000000000}{6500000000000000}.

$$-\frac{1144592482472771339}{6500000000000000}-\frac{45500000000000000}{6500000000000000}=0$$

Since -\frac{1144592482472771339}{6500000000000000} and \frac{45500000000000000}{6500000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1144592482472771339-45500000000000000}{6500000000000000}=0$$

Subtract 45500000000000000 from -1144592482472771339 to get -1190092482472771339.

$$-\frac{1190092482472771339}{6500000000000000}=0$$

Compare -\frac{1190092482472771339}{6500000000000000} and 0.

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