How do you solve using the completing the square method $m^{2} - 10 m = 3$ $m^2 - 10m = 3$ ?

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Answer 1 · 2017-04-26T13:03:19

$m = 10.29 or m = 0.29$ $m = 10.29" or "m = 0.29$

You would like to change the given equation into the form

${(x + b)}^{2} = c$ $(x +b)^2 = c$ so that you can find the square roots and solve.

$m^{2} - 10 m = 3$ $m^2color(blue)(-10)m =3$

Add on ${(\frac{b}{2})}^{2}$ $color(blue)((b/2)^2)$ to both sides: ${(\frac{- 10}{2})}^{2} = 25$ $color(blue)(((-10)/2)^2 = 25)$

$m^{2} - 10 m + 25 = 3 + 25$ $m^2 -10 mcolor(blue)(+25) = 3 color(blue)(+25)$

$color(white)(....)(m-5)^2" " = 28$

$color(white)(.............)m - 5 = +-sqrt28$

$color(white)(....................)m = 5+-sqrt28$

$m = 10.29" or "m = 0.29$

How do you solve using the completing the square method m^2 - 10m = 3m2−10m=3m^2 - 10m = 3?