In the equation, #x-sqrt(x-4)=4#, how do we solve for x, showing the complete solution? Thanks

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Answer 1 · 2017-10-10T06:46:21

x = 4 0r 5

Rewrite the equation as, #- sqrt(x-4) = 4 - x#

squaring both sides, we get
#[-sqrt(x-4)]^2 = (4-x)^2#

#rArr x - 4 = 16 - 8x + x^2#

#rArr x^2-8x-x+16+4 =0 #

#rArr x^2-9x+20 = 0#

#rArr x^2-4x-5x+20 =0#

#rArr x(x-4)-5(x-4)=0#

#rArr(x-4)(x-5)=0#

#rArr (x-4) = 0 and (x-5)=0#

#rArr x = 4 or 5#