kindly help me to solve this equation

how he calculated vlue of d to be 16.1

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- Feb 24th 2011, 07:19 AMmoonnightingalehow value of d is calculated in this equation
kindly help me to solve this equation

how he calculated vlue of d to be 16.1 - Feb 24th 2011, 08:17 AMharish21
$\displaystyle RHS=0.022\times10^{-6}\times 3\times10^8=6.6$

Therefore, you have:

$\displaystyle 2\sqrt{\bigg(\dfrac{d}{2}\bigg)^2+8^2}-d= 6.6$

$\displaystyle 2\sqrt{\bigg(\dfrac{d^2}{4}\bigg)+64}=6.6+d$

squaring both sides gives you:

$\displaystyle \bigg[2\sqrt{\bigg(\dfrac{d^2}{4}\bigg)+64}\bigg]^2=(6.6+d)^2$

$\displaystyle 4 \cdot \bigg(\dfrac{d^2}{4}+64\bigg) = 6.6^2+2d(6.6)+ d^2$

$\displaystyle d^2+256=43.56+13.2d+d^2$

the $\displaystyle d^2$ terms cancel each other out and simplification gives you the value of d.