Solve omega_{2}=0,16=8.56+x/107+x*142/322

$$\omega _ { 2 } = 0,16 = \frac { 8.56 + x } { 107 + x } \cdot \frac { 142 } { 322 }$$

Solve for ω_2, x

$$x = -\frac{6875606}{62625} = -109\frac{49481}{62625} \approx -109.790115768$$

$$\omega _{2}=0$$

Solution Steps

Consider the second equation. Variable x cannot be equal to -107 since division by zero is not defined. Multiply both sides of the equation by 322\left(x+107\right), the least common multiple of 107+x,322.

$$5152\left(x+107\right)=322\left(8.56+x\right)\times \frac{142}{322}$$

Use the distributive property to multiply 5152 by x+107.

$$5152x+551264=322\left(8.56+x\right)\times \frac{142}{322}$$

Reduce the fraction \frac{142}{322} to lowest terms by extracting and canceling out 2.

$$5152x+551264=322\left(8.56+x\right)\times \frac{71}{161}$$

Multiply 322 and \frac{71}{161} to get 142.

$$5152x+551264=142\left(8.56+x\right)$$

Use the distributive property to multiply 142 by 8.56+x.

$$5152x+551264=1215.52+142x$$

Subtract 142x from both sides.

$$5152x+551264-142x=1215.52$$

Combine 5152x and -142x to get 5010x.

$$5010x+551264=1215.52$$

Subtract 551264 from both sides.

$$5010x=1215.52-551264$$

Subtract 551264 from 1215.52 to get -550048.48.

$$5010x=-550048.48$$

Divide both sides by 5010.

$$x=\frac{-550048.48}{5010}$$

Expand \frac{-550048.48}{5010} by multiplying both numerator and the denominator by 100.

$$x=\frac{-55004848}{501000}$$

Reduce the fraction \frac{-55004848}{501000} to lowest terms by extracting and canceling out 8.

$$x=-\frac{6875606}{62625}$$

The system is now solved.

$$\omega _{2}=0 x=-\frac{6875606}{62625}$$