X2-3x-25=(x-2)2

Solution for X2-3x-25=(x-2)2 equation:

X2-3X-25=(X-2)2

We move all terms to the left:

X2-3X-25-((X-2)2)=0

We add all the numbers together, and all the variables

X^2-3X-((X-2)2)-25=0


We calculate terms in parentheses: -((X-2)2), so:

(X-2)2

We multiply parentheses

2X-4

Back to the equation:

-(2X-4)


We get rid of parentheses

X^2-3X-2X+4-25=0

We add all the numbers together, and all the variables

X^2-5X-21=0

a = 1; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·1·(-21)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{109}}{2*1}=\frac{5-\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*1}=\frac{5+\sqrt{109}}{2}
$