What is the sum of the two real solutions to #x+4=sqrt(13x+30)#?

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Answer 1 · 2016-08-17T14:19:34

The sum of the two real solutions equals #5#.

#(x + 4)^2 = (sqrt(13x + 30))^2#

#x^2 + 8x+ 16 = 13x + 30#

#x^2 -5x - 14 = 0#

#(x - 7)(x + 2) = 0#

#x = 7 and -2#

CHECK:

#7 + 4 =^? sqrt(13(7) + 30)#

#11 = sqrt(121)#

#x = 7 ->color(green)("true")#

CHECK:

#-2 + 4 =^? sqrt(13(-2)+ 30)#

#2 = sqrt(4)#

#x = -2 -> color(green)("true")#
Hence, both solutions are just. We can now state the solution set and find the sum of the two real solutions.

SOLUTION SET: #{-2, 7}#

Sum #= -2 + 7 = 5#