How do you solve?

Question

the question asks use factoring and zero-product property to solve x^2+32=12x...i would like to know what steps to take to arrive to the answer......THIS IS ALGEBRA 2!!

Answer 1

*Set the equation to "0" - subtract 12x from both sides (when you move a term to the opposite side, always use the opposite sign).

x^2 + 32 - 12x = 12x - 12x
x^2 - 12x + 32 = 0

First: factor - multiply the 1st & 3rd term to get 32. find two numbers that give you 32 when multiplied & (-12)/2nd term when added/subtracted. the numbers are (-8 & -4). rewrite the expression with the new middle terms.

x^2 - 8x - 4x + 32 = 0

Sec: group "like" terms & factor both sets of parenthesis.

(x^2 - 8x) - (4x + 32) = 0
x(x - 8) - 4(x - 8) = 0
(x - 8)(x - 4) = 0

Third: set both parenthesis to "0" - solve the "x" variables.

a. x - 8 = 0 > add 8 to both sides.
x-8+8 = 0+8
x = 8

b. x - 4 = 0 > add 4 to both sides.
x - 4 + 4 = 0 + 4
x = 4

Solutions: 4, 8

Answer 2

First get it into standard form:
x^2 - 12x + 32 = 0

Now factor. There's a "+" on the end but a "-" in the middle, so that means we have minus signs in both terms:
(x - ?)(x - ?) = 0
We need to find two numbers whose product is 32 and whose sum is -12, to match our original equation. 4 and 8 will work. this gives us
(x - 4)(x - 8) = 0

Since the product of these two expressions is 0, then that means one or the other has to be zero. This happens when x = 8 or x = 4. So that's the solution.

Answer 3

First rearrange the problem so that x^2 -12x + 32 = 0
now you can factor into (x-4)*(x-8) = 0, then one of the two terms, x-4 or x-8, must equal zero sijnce their product equals 0, so there are two possible answers x= 4 or x=8.

Answer 4

x^2+32=12x

Subtract 12x from both sides of the equation
x^2 - 12x + 32 = 0

Factor

(x - 4)(x - 8) = 0

x = 4, x = 8
.

Answer 5

bring everything to one side and...

x^2 - 12x + 32 = 0

what two numbers summed together equal -12 and when multiplied equal +32?

(x - 4)(x - 8) = 0

what values of x make this expression true?

x = 4 and x = 8

Answer 6

x^2+32=12x
1. subtract 12x from each side
x^2 - 12x + 32 = 0
2.seperate
(x - 8)(x - 4) = 0
subtract 8 from zero
x = 8, (x-4)=0
subtract 4 from zero
x=4

or do -b +/- square root of (b^2 -4ac) all over 2

{12 +/- square root of [ (-12)^2 - 4(1)(32) ] } / 2

Answer 7

rearrange

in descending order:

x^2-12x+32=0

(x-8)(x-4)=0
x=8,4

I learned this in algebra 1

Answer 8

x^2+32=12x...
x^2-12x+32=0
()x-4(x-8)=0
x=4,8 answer