how do u make w the sub ject of this equation? 36=(2w+1)w?

Answer 1

36=(2w+1)w

distribute w
36=2w^2+w

bring w 36 over
0=2w^2+w-36

Factor
(2w+9)(w-4)

Find when each factor is 0
2w+9 = 0 w=-9/2
(w-4) = 0 w = 4

w = 4 or w = -9/2

Check
36=(2*4+1)4 9*4 = 36
36=(-9/2*+1)*-9/2 (-9/2)(-8) =36

Alternatively you could have used the quadratic formula
-1 + sqrt(1^2 - 4*2*-36)/(2*2) = 4
-1 - sqrt(1^2 - 4*2*-36)/(2*2) = -9/2

Answer 2

If you mean to solve for w -- then you need to multiply the right hand side first, using the distributive property. This gives you 36 = 2w^2 + w. Then subtract 36 from both sides to get 0 = 2w^2 + w - 36.

This quadratic equation can then be factored as
(2w + 9)(w - 4) = 0. Set each factor equal to 0. This gives you 2 solutions: w = -9/2 or w = 4.

Hope this helps!

Answer 3

2w^2 + w = 36
so 2w^2 + w -36 = 0

We want to factor the polynomial so assume
(2w+a)(w+b) = 0
2w^2 + aw +2bw + ab = 0
2w^2 +(a+2b)w + ab = 0

Therefore ab = -36 a+2b = 1

-36 = 9 x -4 (finding suitable factors of 36)
So if a = 9 and b = -4 we solve the system of equations.

The factorization gives

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

Which means, solving for w that

w = -9/2 or w = 4 are the roots.