(5)^2x+1/25=125

Solution for (5)^2x+1/25=125 equation:

(5)^2x+1/25=125

We move all terms to the left:

(5)^2x+1/25-(125)=0

determiningTheFunctionDomain
5^2x-125+1/25=0

We multiply all the terms by the denominator


5^2x*25+1-125*25=0

We add all the numbers together, and all the variables

5^2x*25-3124=0

Wy multiply elements

125x^2-3124=0

a = 125; b = 0; c = -3124;
Δ = b2-4ac
Δ = 02-4·125·(-3124)
Δ = 1562000
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:

$\sqrt{\Delta}=\sqrt{1562000}=\sqrt{400*3905}=\sqrt{400}*\sqrt{3905}=20\sqrt{3905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3905}}{2*125}=\frac{0-20\sqrt{3905}}{250}
=-\frac{20\sqrt{3905}}{250}
=-\frac{2\sqrt{3905}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3905}}{2*125}=\frac{0+20\sqrt{3905}}{250}
=\frac{20\sqrt{3905}}{250}
=\frac{2\sqrt{3905}}{25}
$