x=-100+(1.1x-11)x

Solution for x=-100+(1.1x-11)x equation:

x=-100+(1.1x-11)x

We move all terms to the left:

x-(-100+(1.1x-11)x)=0


We calculate terms in parentheses: -(-100+(1.1x-11)x), so:

-100+(1.1x-11)x

determiningTheFunctionDomain
(1.1x-11)x-100

We multiply parentheses

x^2-11x-100

Back to the equation:

-(x^2-11x-100)


We get rid of parentheses

-x^2+x+11x+100=0

We add all the numbers together, and all the variables

-1x^2+12x+100=0

a = -1; b = 12; c = +100;
Δ = b2-4ac
Δ = 122-4·(-1)·100
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{34}}{2*-1}=\frac{-12-4\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{34}}{2*-1}=\frac{-12+4\sqrt{34}}{-2}
$