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

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`(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, College Junior | (Level 1) Honors

Posted on

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, Undergraduate | (Level 2) Valedictorian

Posted on

`(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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