(x)(x+1)=35+11(x)+(x+1)

Solution for (x)(x+1)=35+11(x)+(x+1) equation:

(x)(x+1)=35+11(x)+(x+1)

We move all terms to the left:

(x)(x+1)-(35+11(x)+(x+1))=0

We multiply parentheses

x^2+x-(35+11x+(x+1))=0


We calculate terms in parentheses: -(35+11x+(x+1)), so:

35+11x+(x+1)

determiningTheFunctionDomain
11x+(x+1)+35

We get rid of parentheses

11x+x+1+35

We add all the numbers together, and all the variables

12x+36

Back to the equation:

-(12x+36)


We get rid of parentheses

x^2+x-12x-36=0

We add all the numbers together, and all the variables

x^2-11x-36=0

a = 1; b = -11; c = -36;
Δ = b2-4ac
Δ = -112-4·1·(-36)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{265}}{2*1}=\frac{11-\sqrt{265}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{265}}{2*1}=\frac{11+\sqrt{265}}{2}
$