X2+6x+9=(x+3)2

Solution for X2+6x+9=(x+3)2 equation:

X2+6X+9=(X+3)2

We move all terms to the left:

X2+6X+9-((X+3)2)=0

We add all the numbers together, and all the variables

X^2+6X-((X+3)2)+9=0


We calculate terms in parentheses: -((X+3)2), so:

(X+3)2

We multiply parentheses

2X+6

Back to the equation:

-(2X+6)


We get rid of parentheses

X^2+6X-2X-6+9=0

We add all the numbers together, and all the variables

X^2+4X+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$