X2+(2x+1)2=34

Solution for X2+(2x+1)2=34 equation:

X2+(2X+1)2=34

We move all terms to the left:

X2+(2X+1)2-(34)=0

We add all the numbers together, and all the variables

X^2+(2X+1)2-34=0

We multiply parentheses

X^2+4X+2-34=0

We add all the numbers together, and all the variables

X^2+4X-32=0

a = 1; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*1}=\frac{8}{2}
=4
$