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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 ________


Sagot :

Answer:

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

Explanation:

Given

[tex]1.77 * 10^{-2} = \frac{x^2}{0.298 - x}[/tex] --- the actual equation

Required

The values of x

We have:

[tex]1.77 * 10^{-2} = \frac{x^2}{0.298 - x}[/tex]

Cross Multiply

[tex]1.77 * 10^{-2} * (0.298 - x)= x^2[/tex]

Multiply both sides by 100

[tex]1.77 * (0.298 - x)= 100x^2[/tex]

Open bracket

[tex]0.52746 - 1.77x= 100x^2[/tex]

Rewrite as:

[tex]100x^2 + 1.77x - 0.52746 =0[/tex]

Using quadratic formula:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

[tex]a = 100; b = 1.77; c = -0.52746[/tex]

So, we have:

[tex]x = \frac{-1.77 \± \sqrt{1.77^2 - 4*100*- 0.52746 }}{2*100}[/tex]

[tex]x = \frac{-1.77 \± \sqrt{214.1169}}{2*100}[/tex]

[tex]x = \frac{-1.77 \± 14.63}{200}[/tex]

Split

[tex]x = \frac{-1.77 + 14.63}{200}\ or\ x = \frac{-1.77 - 14.63}{200}[/tex]

[tex]x = \frac{12.86}{200}\ or\ x = \frac{-16.40}{200}[/tex]

[tex]x = 0.0643\ or\ x = -0.082[/tex]

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