Question

Many chemistry problems result in equations of the form

Answer 1

Answer:

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

Explanation:

Given

$1.77 * 10^{-2} = \frac{x^2}{0.298 - x}$ --- the actual equation

Required

The values of x

We have:

$1.77 * 10^{-2} = \frac{x^2}{0.298 - x}$

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:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where:

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

So, we have:

$x = \frac{-1.77 \± \sqrt{1.77^2 - 4*100*- 0.52746 }}{2*100}$

$x = \frac{-1.77 \± \sqrt{214.1169}}{2*100}$

$x = \frac{-1.77 \± 14.63}{200}$

Split

$x = \frac{-1.77 + 14.63}{200}\ or\ x = \frac{-1.77 - 14.63}{200}$

$x = \frac{12.86}{200}\ or\ x = \frac{-16.40}{200}$

$x = 0.0643\ or\ x = -0.082$