X^2+2x+1=675

Solution for X^2+2x+1=675 equation:

X^2+2X+1=675

We move all terms to the left:

X^2+2X+1-(675)=0

We add all the numbers together, and all the variables

X^2+2X-674=0

a = 1; b = 2; c = -674;
Δ = b2-4ac
Δ = 22-4·1·(-674)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30\sqrt{3}}{2*1}=\frac{-2-30\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30\sqrt{3}}{2*1}=\frac{-2+30\sqrt{3}}{2}
$