(x2+1)2+2(x2+1)-35=0

Solution for (x2+1)2+2(x2+1)-35=0 equation:

(x2+1)2+2(x2+1)-35=0

We add all the numbers together, and all the variables

(+x^2+1)2+2(+x^2+1)-35=0

We multiply parentheses

2x^2+2x^2+2+2-35=0

We add all the numbers together, and all the variables

4x^2-31=0

a = 4; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·4·(-31)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{31}}{2*4}=\frac{0-4\sqrt{31}}{8}
=-\frac{4\sqrt{31}}{8}
=-\frac{\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{31}}{2*4}=\frac{0+4\sqrt{31}}{8}
=\frac{4\sqrt{31}}{8}
=\frac{\sqrt{31}}{2}
$