Solve for the indicated variable.
$m=\dfrac{1}{2}\sqrt{2a^2+2b^2-2c^2}$ for a0

Question

Solve for the indicated variable.
$m=\dfrac{1}{2}\sqrt{2a^2+2b^2-2c^2}$ for a>0

Quizlet Admin · Accepted Answer

$$\displaylines{
  m = \frac{1}{2}\sqrt {2{a^2} + 2{b^2} - 2{c^2}} ,{	ext{ solve for }}a > 0 \cr 
  	extcolor{Blue}{{	ext{Multiply both sides by 2}}} \cr 
  2m = \sqrt {2{a^2} + 2{b^2} - 2{c^2}}  \cr 
  	extcolor{Blue}{{	ext{Raise both sides to the second power}}} \cr 
  {\left( {2m} ight)^2} = {\left( {\sqrt {2{a^2} + 2{b^2} - 2{c^2}} } ight)^2} \cr 
  	extcolor{Blue}{{	ext{Simplify}}} \cr 
  4{m^2} = 2{a^2} + 2{b^2} - 2{c^2} \cr 
	extcolor{Blue}{  {	ext{Subtract }}2{b^2} - 2{c^2}{	ext{ from each side}}} \cr 
  4{m^2} - 2{b^2} + 2{c^2} = 2{a^2} \cr 
 	extcolor{Blue}{ {	ext{Divide each side by 2}}} \cr 
  2{m^2} - {b^2} + {c^2} = {a^2} \cr 
  	extcolor{Blue}{{	ext{Take square root of each side}}} \cr 
   \pm \sqrt {2{m^2} - {b^2} + {c^2}}  = \sqrt {{a^2}}  \cr 
  a =  \pm \sqrt {2{m^2} - {b^2} + {c^2}}  \cr 
  	extcolor{Blue}{{	ext{Since }}a > 0,{	ext{ we take the positive square root only}}} \cr 
  a = \sqrt {2{m^2} - {b^2} + {c^2}} {	ext{ }} \cr} $$

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