Question

How do you solve `2w ^ { 2} + 4w + 11= ( w - 2) ^ { 2}`?

Answer 1

`w=-1 or w=-7`

Explanation:

• Firstly expand the right side:
  `(w-2)^2 = (w-2)(w-2)=w^2-4w+4`

• subtract `w^2-4w+4` from both sides:
  `w^2+8w+7=0`

• factor the left side
  `(w+7)(w+1)=0`

• By the zero product property
  `(w+7) = 0 or (w+1) = 0`

`w+7=0`
`w=-7`

`w+1=0`
`w=-1`

graph{y=(x+7)(x+1) [-20, 20, -10, 10]}