2(w^2)+10w+9=(w+2)(w+2)

Solution for 2(w^2)+10w+9=(w+2)(w+2) equation:

2(w^2)+10w+9=(w+2)(w+2)

We move all terms to the left:

2(w^2)+10w+9-((w+2)(w+2))=0

We multiply parentheses ..

2w^2-((+w^2+2w+2w+4))+10w+9=0


We calculate terms in parentheses: -((+w^2+2w+2w+4)), so:

(+w^2+2w+2w+4)

We get rid of parentheses

w^2+2w+2w+4

We add all the numbers together, and all the variables

w^2+4w+4

Back to the equation:

-(w^2+4w+4)


We add all the numbers together, and all the variables

2w^2+10w-(w^2+4w+4)+9=0

We get rid of parentheses

2w^2-w^2+10w-4w-4+9=0

We add all the numbers together, and all the variables

w^2+6w+5=0

a = 1; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*1}=\frac{-10}{2}
=-5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*1}=\frac{-2}{2}
=-1
$