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(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} $
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