5^(2x)=1/25

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

5^(2x)=1/25

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5^2x-1/25=0

We multiply all the terms by the denominator


5^2x*25-1=0

Wy multiply elements

125x^2-1=0

a = 125; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·125·(-1)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*125}=\frac{0-10\sqrt{5}}{250}
=-\frac{10\sqrt{5}}{250}
=-\frac{\sqrt{5}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*125}=\frac{0+10\sqrt{5}}{250}
=\frac{10\sqrt{5}}{250}
=\frac{\sqrt{5}}{25}
$