How do you solve the proportion #(x-1)/4 = 5/(x+7)#?

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Answer 1 · 2016-05-16T10:38:10

#x=-3+-2i#

Cross multiply#" "->" "(x-1)(x+7)=20#

#x^2+6x-7=20#

#x^2+6x+13=0#

Complete the square

#(x+3)^2+13+k=0#

#k=(-1)xx3^2=-9#

#(x+3)^2+4=0#

#x+3=+-sqrt(-4)#

There is no solution for the set of numbers 'Real' #->x!inRR#
There is a solution for the set of numbers 'Complex' #->x inCC#

#x+3=+-2i#

#x=-3+-2i#

Tony B