How do you solve #\sqrt { - 38z } = \sqrt { - 37z + 34}#?

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Answer 1 · 2018-01-26T14:59:36

See a solution process below:

First, square each side of the equation to eliminate the radical while keeping the equation balanced:

#(sqrt(-38z))^2 = (sqrt(-37z + 34))^2#

#-38z = -37z + 34#

Now, add #color(red)(38z)# and subtract #color(blue)(34)# from each side of the equation to solve for #z# while keeping the equation balanced:

#-38z + color(red)(38z) - color(blue)(34) = -37z + color(red)(38z) + 34 - color(blue)(34)#

#0 - 34 = (-37 + color(red)(38))z + 0#

#-34 = 1z#

#-34 = z#

#x = -34#