(X+5)=(x+1)(x+1)

Solution for (X+5)=(x+1)(x+1) equation:

(X+5)=(X+1)(X+1)

We move all terms to the left:

(X+5)-((X+1)(X+1))=0

We get rid of parentheses

X-((X+1)(X+1))+5=0

We multiply parentheses ..

-((+X^2+X+X+1))+X+5=0


We calculate terms in parentheses: -((+X^2+X+X+1)), so:

(+X^2+X+X+1)

We get rid of parentheses

X^2+X+X+1

We add all the numbers together, and all the variables

X^2+2X+1

Back to the equation:

-(X^2+2X+1)


We add all the numbers together, and all the variables

X-(X^2+2X+1)+5=0

We get rid of parentheses

-X^2+X-2X-1+5=0

We add all the numbers together, and all the variables

-1X^2-1X+4=0

a = -1; b = -1; c = +4;
Δ = b2-4ac
Δ = -12-4·(-1)·4
Δ = 17
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{-(-1)-\sqrt{17}}{2*-1}=\frac{1-\sqrt{17}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*-1}=\frac{1+\sqrt{17}}{-2}
$