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x^2+6x+6=2
We move all terms to the left:
x^2+6x+6-(2)=0
We add all the numbers together, and all the variables
x^2+6x+4=0
a = 1; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·1·4
Δ = 20
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*1}=\frac{-6-2\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*1}=\frac{-6+2\sqrt{5}}{2} $
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