Question

Many chemistry problems result in equations of the form

1.77 X100.298-z)
When this equation is solved, the two values of the unknown are ________ and ________

Answer 1

When this equation is solved, the two values of the unknown are 0.0643 and -0.082

Step-by-step explanation:

Given

`1.77 * 10^(-2) = (x^2)/(0.298 - x)` --- the actual equation

Required

The values of x

We have:

`1.77 * 10^(-2) = (x^2)/(0.298 - x)`

Cross Multiply

`1.77 * 10^(-2) * (0.298 - x)= x^2`

Multiply both sides by 100

`1.77 * (0.298 - x)= 100x^2`

Open bracket

`0.52746 - 1.77x= 100x^2`

Rewrite as:

`100x^2 + 1.77x - 0.52746 =0`

Using quadratic formula:

`x = (-b \± √(b^2 - 4ac))/(2a)`

Where:

`a = 100; b = 1.77; c = -0.52746`

So, we have:

`x = (-1.77 \± √(1.77^2 - 4*100*- 0.52746 ))/(2*100)`

`x = (-1.77 \± √(214.1169))/(2*100)`

`x = (-1.77 \± 14.63)/(200)`

Split

`x = (-1.77 + 14.63)/(200)\ or\ x = (-1.77 - 14.63)/(200)`

`x = (12.86)/(200)\ or\ x = (-16.40)/(200)`

`x = 0.0643\ or\ x = -0.082`