Solve for x: (hint: factor) x2-8x+12=0

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You also may substitute `16-4`  for `12`  such that:

`x^2 - 8x + 16 - 4 = 0`

You need to group the terms such that:

`(x^2 - 4) + (-8x + 16) = 0`

You should convert the difference of squares `x^2 - 4`  into a product using the following formula such that:

`a^2 - b^2 = (a-b)(a+b)` 

Reasoning by analogy yields:

`x^2 - 4 = (x-2)(x+2)`

You need to factor out -8 in the group of terms -`8x + 16`  such that:

`(x-2)(x+2) - 8(x-2) = 0`

Factoring out `x-2`  yields:

`(x-2)(x+2-8) = 0`

You should remember that a product yields 0 if one of the factors is zero such that:

`x-2=0 => x=2`

`x-6=0 => x=6`

Hence, evaluating the solutions to quadratic equation, using the factored form, yields x=2 and `x=6` .

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial