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a*a*2-512=0
Wy multiply elements
2a^2*2-512=0
Wy multiply elements
4a^2-512=0
a = 4; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·4·(-512)
Δ = 8192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*4}=\frac{0-64\sqrt{2}}{8} =-\frac{64\sqrt{2}}{8} =-8\sqrt{2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*4}=\frac{0+64\sqrt{2}}{8} =\frac{64\sqrt{2}}{8} =8\sqrt{2} $
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