X^2-2x+1=9/25

Solution for X^2-2x+1=9/25 equation:

X^2-2X+1=9/25

We move all terms to the left:

X^2-2X+1-(9/25)=0

We add all the numbers together, and all the variables

X^2-2X+1-(+9/25)=0

We get rid of parentheses

X^2-2X+1-9/25=0

We multiply all the terms by the denominator


X^2*25-2X*25-9+1*25=0

We add all the numbers together, and all the variables

X^2*25-2X*25+16=0

Wy multiply elements

25X^2-50X+16=0

a = 25; b = -50; c = +16;
Δ = b2-4ac
Δ = -502-4·25·16
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-30}{2*25}=\frac{20}{50}
=2/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+30}{2*25}=\frac{80}{50}
=1+3/5
$