How do you find the roots, real and imaginary, of #y= x^2 -21x +(x+1)^2 # using the quadratic formula?

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Answer 1 · 2017-08-10T07:14:17

#x = frac(19 pm sqrt(353))(4)#

We have: #y = x^(2) - 21 x + (x + 1)^(2)#

First, let's expand the parentheses:

#Rightarrow y = x^(2) - 21 x + x^(2) + 2 x + 1#

#Rightarrow y = 2 x^(2) - 19 x + 1#

Then, let's apply the quadratic formula:

#Rightarrow x = frac(- (- 19) pm sqrt((- 19)^(2) - 4(2)(1)))(2(2))#

#Rightarrow x = frac(19 pm sqrt(361 - 8))(4)#

#Rightarrow x = frac(19 pm sqrt(353))(4)#

Therefore, the solutions to the equation are #x = frac(19 - sqrt(353))(4)# and #x = frac(19 + sqrt(353))(4)#.