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(x+9)(x-11)/(x+7)=0
Domain of the equation: (x+7)!=0We multiply parentheses ..
We move all terms containing x to the left, all other terms to the right
x!=-7
x∈R
(+x^2-11x+9x-99)/(x+7)=0
We multiply all the terms by the denominator
(+x^2-11x+9x-99)=0
We get rid of parentheses
x^2-11x+9x-99=0
We add all the numbers together, and all the variables
x^2-2x-99=0
a = 1; b = -2; c = -99;
Δ = b2-4ac
Δ = -22-4·1·(-99)
Δ = 400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-20}{2*1}=\frac{-18}{2} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+20}{2*1}=\frac{22}{2} =11 $
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