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x^2-100x+81=0
a = 1; b = -100; c = +81;
Δ = b2-4ac
Δ = -1002-4·1·81
Δ = 9676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9676}=\sqrt{4*2419}=\sqrt{4}*\sqrt{2419}=2\sqrt{2419}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2419}}{2*1}=\frac{100-2\sqrt{2419}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2419}}{2*1}=\frac{100+2\sqrt{2419}}{2} $
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