z2=593

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Solution for z2=593 equation:



z2=593
We move all terms to the left:
z2-(593)=0
We add all the numbers together, and all the variables
z^2-593=0
a = 1; b = 0; c = -593;
Δ = b2-4ac
Δ = 02-4·1·(-593)
Δ = 2372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{593}}{2*1}=\frac{0-2\sqrt{593}}{2} =-\frac{2\sqrt{593}}{2} =-\sqrt{593} $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{593}}{2*1}=\frac{0+2\sqrt{593}}{2} =\frac{2\sqrt{593}}{2} =\sqrt{593} $

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