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

sciencesolve | Teacher | (Level 3) Educator Emeritus

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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` .

mehta1996 | Student, Grade 10 | eNotes Newbie

Posted on

x2-8x+12=0

(split the middle term such that when you multiply the coeffecients of the x you get the constant (12))

x2-6x-2x+12=0

Take the common elements out

x(x-6)-2(x-6)=0

(x-2)(x-6)=0

therefore,

x=2 or x=6