1/2x^2+11=38

Solution for 1/2x^2+11=38 equation:

1/2x^2+11=38

We move all terms to the left:

1/2x^2+11-(38)=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^2-27=0

We multiply all the terms by the denominator


-27*2x^2+1=0

Wy multiply elements

-54x^2+1=0

a = -54; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-54)·1
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-54}=\frac{0-6\sqrt{6}}{-108}
=-\frac{6\sqrt{6}}{-108}
=-\frac{\sqrt{6}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-54}=\frac{0+6\sqrt{6}}{-108}
=\frac{6\sqrt{6}}{-108}
=\frac{\sqrt{6}}{-18}
$