(1/x^2)+10=35

Solution for (1/x^2)+10=35 equation:

(1/x^2)+10=35

We move all terms to the left:

(1/x^2)+10-(35)=0


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(1/x^2)-25=0

We get rid of parentheses

1/x^2-25=0

We multiply all the terms by the denominator


-25*x^2+1=0

We add all the numbers together, and all the variables

-25x^2+1=0

a = -25; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-25)·1
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-25}=\frac{-10}{-50}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-25}=\frac{10}{-50}
=-1/5
$