How do you solve using the completing the square method #z^2 + 10z = -24#?

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Answer 1 · 2016-03-04T13:56:55

The solutions are:

#color(green)(z = -4#
# color(green)(z =-6#

#z^2+10z= -24#

To write the Left Hand Side as a Perfect Square, we add 25 to both sides
#z^2+10z +25= -24 +25#

#z^2 + 2*5*z + 5^2 = 1#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(z+5)^2 = 1#

#z + 5 = + sqrt1 =1#
#color(green)(z =1 - 5= -4#

or,

#z +5 = -sqrt1= -1#
#color(green)(z = -1 -5=-6#