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

Aug 19, 2017

$m = - 0.9 + \sqrt{2.31}$ and $m = - 0.9 - \sqrt{2.31}$

#### Explanation:

First: ${\left(m + 0.9\right)}^{2} = 0$
Put m + (half of 1.8) in a bracket and square them

This expands to ${m}^{2} + 1.8 m + 0.81$. 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
${\left(m + 0.9\right)}^{2} - \left(0.81 + 1.5\right) = 0$
${\left(m + 0.9\right)}^{2} - 2.31 = 0$

Now move the -2.31 to the other side
${\left(m + 0.9\right)}^{2} = 2.31$

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

Move the 0.9 to rhs
m=-0.9±sqrt2.31