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

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

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Answer 1 · 2017-08-19T22:21:17

$m = - 0.9 + \sqrt{2.31}$ $m= -0.9 + sqrt2.31$ and $m = - 0.9 - \sqrt{2.31}$ $m=-0.9-sqrt2.31$

Explanation:

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

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

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

Square root both sides
$m + 0.9 = \pm \sqrt{2.31}$ $m+0.9=±sqrt2.31$

Move the 0.9 to rhs
$m = - 0.9 \pm \sqrt{2.31}$ $m=-0.9±sqrt2.31$

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

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Explanation:

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How do you solve m2+1.8m−1.5=0m^2+1.8m-1.5=0 by completing the square?

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