How do you solve #m^2+1.8m-1.5=0# by completing the square?

1 Answer
Aug 19, 2017

Answer:

#m= -0.9 + sqrt2.31# and #m=-0.9-sqrt2.31#

Explanation:

First: #(m+0.9)^2 =0#
Put m + (half of 1.8) in a bracket and square them

This expands to #m^2 +1.8m+0.81#. Note that this is almost what we started with - only the c value, 0.81, is wrong. We want it to be -1.5, so we adjust for this by subtracting 0.81 and 1.5

This makes it
#(m+0.9)^2 -(0.81+1.5)=0#
#(m+0.9)^2-2.31=0#

Now move the -2.31 to the other side
#(m+0.9)^2=2.31#

Square root both sides
#m+0.9=±sqrt2.31#

Move the 0.9 to rhs
#m=-0.9±sqrt2.31#