Can someone help me with math homework? (2ω-3)^2 - (ω-2)^2=2ω^2-11

Expert Answers
lemjay eNotes educator| Certified Educator

`(2w-3)^2-(w-2)^2=2w^2-11`

To solve it, first expand the binomials. To expand them, apply FOIL.

`(2w-3)(2w-3) - (w-2)(w-2)=2w^2-11`

`4w^2 -12w+9 - (w^2-4w+4) = 2w^2 -11`

`4w^2 -12w+9 -w^2 +4w -4=2w^2-11`

Then, combine like terms to simplify the left side of the equation.

`3w^2 -8w +5=2w^2 -11`

Since it is a quadratic equation, to solve it, set one side equal to zero. So, subtract both sides by 2w^2 -11.

`3w^2 -8w + 5 - (2w^2 - 11) = 2w^2 - 11 - (2w^2 -11)`

`3w^2 - 8w + 5 - 2w^2 +11 = 0`

`w^2 - 8w + 16 = 0`

Then, factor it.

`(w - 4)(w - 4) = 0`

`(w-4)^2 = 0`

Take the square root of both sides to have w-4 only at the left. 

`sqrt((w-4)^2)=+-sqrt0`

`w=4`

Thus, solution to the given equation is `w=4` .

steamgirl | Student

Alright first use the box method to solve out the fist two exponential functions, as shown in image, multiply each row and column. You end up with:

(4w^2 - 12w +9) - (w^2 -4w +4) = 2w^2 -11

Simplify and combine like terms:

3w^2 -8w + 5 = 2w^2 - 11

w^2 - 8w + 16 = 0

Factor:

(w-4)^2 = 0

w = 4

Some images are still being reviewed.
Wiggin42 | Student

`(2w-3)^2 - (w-2)^2=2w^2-11`

` `

`(4w^2 - 12w + 9) - (w^2 - 4w + 4) = 2w^2 - 11`

`3w^2 - 8w + 5 = 2w^2 - 11`

`w^2 - 8w - 16 = 0`

`(w - 4)(w - 4) = 0`

`w - 4 = 0`

`w = 0 + 4 = 4`

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