Question 213918
Solve by using the quadratic formula. 


{{{(18/w^2) - (10/w) + 1 = 0 }}}


If your answer contains a radical, express it in simplified form.
Do not convert to decimal form.


Step 1.   Multiply by {{{w^2}}} to get rid of denominators


{{{(w^2*(18/w^2) - (10/w) + 1) = 0}}}


{{{18 - 10w + w^2) = 0}}}


OR


{{{w^2-10w+18}}}


Step 2.   Using the quadratic formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=1, b=-10 and c=18 yields the following steps


*[invoke quadratic "x", 1,-10, 18 ]


Step 4.  Based on the above steps we can simplify the solutions as follows


{{{x1=(10+sqrt(28))/2}}}


{{{x1=(5+sqrt(7*4))/2}}}


{{{x1=5+2sqrt(7)/2}}}


{{{x1=5+sqrt(7)}}}


AND


{{{x2=(10-sqrt(28))/2}}}


{{{x2=(5-sqrt(7*4))/2}}}


{{{x2=5-2sqrt(7/2)}}}


{{{x2=5-sqrt(7)}}}


Step 5. ANSWER:  So solutions are {{{x1=5+sqrt(7)}}} and  {{{x2=5-sqrt(7)}}}


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J