-(x^2+2x+1)=-50

Solution for -(x^2+2x+1)=-50 equation:

-(x^2+2x+1)=-50

We move all terms to the left:

-(x^2+2x+1)-(-50)=0

We add all the numbers together, and all the variables

-(x^2+2x+1)+50=0

We get rid of parentheses

-x^2-2x-1+50=0

We add all the numbers together, and all the variables

-1x^2-2x+49=0

a = -1; b = -2; c = +49;
Δ = b2-4ac
Δ = -22-4·(-1)·49
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{2}}{2*-1}=\frac{2-10\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{2}}{2*-1}=\frac{2+10\sqrt{2}}{-2}
$