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x+4/x+12=-10
We move all terms to the left:
x+4/x+12-(-10)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+4/x+22=0
We multiply all the terms by the denominator
x*x+22*x+4=0
We add all the numbers together, and all the variables
22x+x*x+4=0
Wy multiply elements
x^2+22x+4=0
a = 1; b = 22; c = +4;
Δ = b2-4ac
Δ = 222-4·1·4
Δ = 468
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{13}}{2*1}=\frac{-22-6\sqrt{13}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{13}}{2*1}=\frac{-22+6\sqrt{13}}{2} $
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