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n2+4=175
We move all terms to the left:
n2+4-(175)=0
We add all the numbers together, and all the variables
n^2-171=0
a = 1; b = 0; c = -171;
Δ = b2-4ac
Δ = 02-4·1·(-171)
Δ = 684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*1}=\frac{0-6\sqrt{19}}{2} =-\frac{6\sqrt{19}}{2} =-3\sqrt{19} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*1}=\frac{0+6\sqrt{19}}{2} =\frac{6\sqrt{19}}{2} =3\sqrt{19} $
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