1/2x^2-11=25

Solution for 1/2x^2-11=25 equation:

1/2x^2-11=25

We move all terms to the left:

1/2x^2-11-(25)=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x^2-36=0

We multiply all the terms by the denominator


-36*2x^2+1=0

Wy multiply elements

-72x^2+1=0

a = -72; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-72)·1
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-72}=\frac{0-12\sqrt{2}}{-144}
=-\frac{12\sqrt{2}}{-144}
=-\frac{\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-72}=\frac{0+12\sqrt{2}}{-144}
=\frac{12\sqrt{2}}{-144}
=\frac{\sqrt{2}}{-12}
$