20*20+8*8=c*c

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Solution for 20*20+8*8=c*c equation:



20*20+8*8=c*c
We move all terms to the left:
20*20+8*8-(c*c)=0
We add all the numbers together, and all the variables
-(+c*c)+20*20+8*8=0
We add all the numbers together, and all the variables
-(+c*c)+464=0
We get rid of parentheses
-c*c+464=0
Wy multiply elements
-1c^2+464=0
a = -1; b = 0; c = +464;
Δ = b2-4ac
Δ = 02-4·(-1)·464
Δ = 1856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*-1}=\frac{0-8\sqrt{29}}{-2} =-\frac{8\sqrt{29}}{-2} =-\frac{4\sqrt{29}}{-1} $
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*-1}=\frac{0+8\sqrt{29}}{-2} =\frac{8\sqrt{29}}{-2} =\frac{4\sqrt{29}}{-1} $

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