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z^2=10

We move all terms to the left:

z^2-(10)=0

a = 1; b = 0; c = -10;

Δ = b^{2}-4ac

Δ = 0^{2}-4·1·(-10)

Δ = 40

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{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*1}=\frac{0-2\sqrt{10}}{2} =-\frac{2\sqrt{10}}{2} =-\sqrt{10} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*1}=\frac{0+2\sqrt{10}}{2} =\frac{2\sqrt{10}}{2} =\sqrt{10} $

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