Question 479425
<font face="Times New Roman" size="+2">


Step 1:  Put constant in the RHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 36x^2\ +\ 18x\ =\ -1]


Step 2:  Divide by the lead coefficient:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \frac{1}{2}x\ \ \ =\ -\frac{1}{36}]


Step 3:  Divide the 1st degree term coefficient by 2, square the result, then add that result to both sides of the equation.  Collect terms on the right.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \frac{1}{2}x\ +\ \frac{1}{16}\ =\ -\frac{1}{36}\ +\ \frac{1}{16}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \frac{1}{2}x\ +\ \frac{1}{16}\ =\ \frac{5}{144}]


You had better check my arithmetic.  It is simply foolish to trust someone you don't know not to make simple arithmetic errors.


Step 4:  Factor the perfect square trinomial in the LHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ \frac{1}{4}\right)^2\ =\ \frac{5}{144}]


Step 5:  Take the square root of both sides, remembering to consider both positive and negative roots:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ \frac{1}{4}\ =\ \pm\ \frac{\sqrt{5}}{12}]


Step 6: Add the opposite of the constant in the LHS to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -\frac{1}{4}\ \pm\ \frac{\sqrt{5}}{12}]


Step 7:  Apply LCD and add fractions in the RHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-3\ \pm\ \sqrt{5}}{12}]


Step 8: Check your ID.  If you were born on or before this date in 1990, go have a beer. Otherwise celebrate in a more age appropriate way.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>