Question

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

Answer 1

`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`