college algebra function problems4

label Mathematics
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i am stuck on the following problem. here is a pic of the problem

http://imgur.com/Dcg33ok

any help would be appreciated

Oct 19th, 2017

x^2 = 2x + 10

x^2 - 2x - 10 = 0

Using quadratic formula, we get

x = (- b ± √b^2 - 4ac)/2a

Now

x = (- (-2) ± √(-2)^2 - 4(-2)(-10)) / 2(2)

x = ( 2 ± √4 - 80) / 4

x = ( 2 ± √-76) / 4

x = ( 2 ± √-4*19) / 4

x = ( 2 ± 2√-19) / 4

x = 2(1 ± √19i) / 4

x = (1 ± √19i) / 2

Hence the roots are x = { (1 + √19i)/2 , (1 - √19i)/2 }

Nov 19th, 2014

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