F(x)=(x-1)(x-1)

Solution for F(x)=(x-1)(x-1) equation:

(F)=(F-1)(F-1)

We move all terms to the left:

(F)-((F-1)(F-1))=0

We multiply parentheses ..

-((+F^2-1F-1F+1))+F=0


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

(+F^2-1F-1F+1)

We get rid of parentheses

F^2-1F-1F+1

We add all the numbers together, and all the variables

F^2-2F+1

Back to the equation:

-(F^2-2F+1)


We add all the numbers together, and all the variables

F-(F^2-2F+1)=0

We get rid of parentheses

-F^2+F+2F-1=0

We add all the numbers together, and all the variables

-1F^2+3F-1=0

a = -1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-1)·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{5}}{2*-1}=\frac{-3-\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*-1}=\frac{-3+\sqrt{5}}{-2}
$