25=1/2(5)(x^2)

Solution for 25=1/2(5)(x^2) equation:

25=1/2(5)(x^2)

We move all terms to the left:

25-(1/2(5)(x^2))=0


Domain of the equation: 25x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/25x^2+25=0

We multiply all the terms by the denominator


25*25x^2-1=0

Wy multiply elements

625x^2-1=0

a = 625; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·625·(-1)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50}{2*625}=\frac{-50}{1250}
=-1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50}{2*625}=\frac{50}{1250}
=1/25
$