How do you solve $36 = 4 sqrt(4m^2+5)$ ?

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Answer 1 · 2018-03-25T07:07:53

The two solutions are $m=+-sqrt19$ .

$36=4sqrt(4m^2+5)$

$color(blue)(color(black)36/4)=color(blue)(color(black)(4sqrt(4m^2+5))/4)$

$color(blue)(color(black)36/4)=color(blue)(color(black)(color(red)cancelcolor(Black)4sqrt(4m^2+5))/color(red)cancelcolor(black)4)$

$color(blue)(color(black)36/4)=sqrt(4m^2+5)$

$9=sqrt(4m^2+5)$

$9^2=(sqrt(4m^2+5))^2$

$9^2=4m^2+5$

$81=4m^2+5$

$76=4m^2$

$color(blue)(color(black)76/4)=color(blue)(color(black)(4m^2)/4)$

$color(blue)(color(black)76/4)=color(blue)(color(black)(color(red)cancelcolor(black)4m^2)/color(red)cancelcolor(black)4)$

$19=m^2$

$+-sqrt19=sqrt(m^2)$

$m=+-sqrt19$

These are the solutions. Hope this helped!

How do you solve 36 = 4 sqrt(4m^2+5)36 = 4 sqrt(4m^2+5)?