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Answer 1 · 2017-05-01T22:43:25

# x=3,-5 #

By Pythagoras, we have:

# AB^2 = (x-(-1))^2 + (7-4)^2 #

And so:

# 5^2 = (x+1)^2 + 3^2 #
# :. 25 = x^2+2x+1+9 #
# :. x^2+2x-15=0 #
# :. (x+5)(x-3)=0 #

Leading to the two possible solutions:

# x=3,-5 #

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Answer 2 · 2017-05-01T22:50:57

x = 3 or -5

Find the distance between A and B in terms of x and equate it to 5.

To do that, we use Pythagoras' Theorem.

#(x-(-1))^2 + (7-4)^2 = 5^2 #
#(x+1)^2 + 9 = 25#
#(x+1)^2 = 16#
#(x+1) = +- 4#
#x = 3 or -5#