How do you find the roots, real and imaginary, of #y= x^2 - 8x -9- (2x-1)^2 # using the quadratic formula?

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Answer 1 · 2017-12-22T09:38:26

see below

#x^2−8x−9−(2x−1)^2#

#=>x^2−8x−9−(4x^2-2x+1)#

#=>x^2−8x−9−4x^2+2x-1)#

#=>-3x^2−6x−10#

#=>3x^2+6x+10#

#D=b^2-4acquad=>quad36-4*3*10#
#D<0=36-120=-84#

#x_(1,2)=(-b+-sqrtD)/(2a)=(-6+-sqrt(7*3*2*2*i^2))/(6)#

#x_(1,2)=(-6+-2isqrt(7*3))/(6)=(cancel2(-3+-isqrt(21)))/(cancel2*3)#

#x_(1)=(-3-isqrt(21))/(3)=-1-(isqrt(21))/3#

#x_(2)=(-3+isqrt(21))/(3)=-1+(isqrt(21))/3#