x(x+2)=55+5(x+x+2)

Solution for x(x+2)=55+5(x+x+2) equation:

x(x+2)=55+5(x+x+2)

We move all terms to the left:

x(x+2)-(55+5(x+x+2))=0

We add all the numbers together, and all the variables

x(x+2)-(55+5(2x+2))=0

We multiply parentheses

x^2+2x-(55+5(2x+2))=0


We calculate terms in parentheses: -(55+5(2x+2)), so:

55+5(2x+2)

determiningTheFunctionDomain
5(2x+2)+55

We multiply parentheses

10x+10+55

We add all the numbers together, and all the variables

10x+65

Back to the equation:

-(10x+65)


We get rid of parentheses

x^2+2x-10x-65=0

We add all the numbers together, and all the variables

x^2-8x-65=0

a = 1; b = -8; c = -65;
Δ = b2-4ac
Δ = -82-4·1·(-65)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*1}=\frac{26}{2}
=13
$