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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]