Solve for x: x^2-7x+12=0?

Answer 1

The easiest way is to factor into two binomials.
(x - 4)(x - 3) = 0 Set each binomial equal to zero
x - 4 = 0 x - 3 = 0
x = {4,3}

Answer 2

That is easy. (x-3)(x-4) = 0

Thus, x = 3 and x = 4 both work.

You solve this by factoring the equation. It is not easy to explain this process in text.

Think of it as Ax^2+Bx+C where A, B, and C are actual values. Find the factors of A and C. In this case, A is 1 and factors into 1 x 1, and C is 12 and factors to 1x12, 2x6, and 3x4. Also, a negative times a negative is a positive, so -1x-1 also equals 1 and -1x-12, -2x-6, and -3x-4 equal 12 too. Find a combination of 1x12, 2x6, and 3x4 that adds to -7. The only combination is -3x-4.

This is quite complicated at first, but after some time of understanding, it will make sense. Just multiply out (x-3)(x-4) and figure out why it equals x^2 - 7x + 12.

If you need more help, ask for a tutor. Homework is there for you to practice and make wrong answers. Any teacher that determines any amount of your final grade from homework is a failure.

Answer 3

You have to factor.

x^2 - 7x + 12 = 0
(x - 3)(x - 4) = 0
x = 3, 4

Answer 4

x^2-7x+12=0
x^2-4x-3x+12=0
x(x-4)-3(x-4)=0
(x-3)(x-4)=0
x-3=0 x-4=0
x=3 x=4
the solution set is {3,4}

Answer 5

x^2-7x+12=0
(x-3)(x-4)=0
x-3=0; x=3
x-4=0; x=4

Answer 6

First, write out the binomials like this:
(x )(x )=0

What you have to do is figure out what to put for the numbers and whether to put a + or - in between. Here's a shortcut.

Look at the 2nd plus/minus first. This tells you whether the pluses/minuses in the factored form are the same or different. If #1 is (plus), both are the same, and you look at the 1st plus/minus to find out which it is. Then you find pairs of factors on the 3rd term that add up to the coefficient on the 2nd term.

So in this case, since the 3rd term is positive (plus), both plus/minuses are the same. We then look at the 1st plus/minus, which is minus, so the binomial terms in the factored form have minuses. So it looks like this: (x -___)(x -___)

Now we need to find the pair of factors of 12 with a sum of 7.
1 + 12 = 13 nope
2 + 6 = 8 nope
3 + 4 = 7 bingo. Fill those in.

So factored form is (x-3)(x-4) = 0.
and x is either 3 or 4 (either one will make one term 0 and thus the whole product).

If the 2nd plus/minus was a minus, then the plus/minuses in the factored form are *different*. We then look for factor pairs with a *difference* that equals the 2nd term, and put the 1st plus/minus on the larger of the two numbers.

Think minus/different/difference and plus/same/sum.

Answer 7

Number one.. You should do your own homework.. But heres a hint . You have to figure out how to get all the variables on the same side. So plan on throwing the 12 to the other side of the "=" as a -12 and work from there.

Answer 8

its so simple

x can be 4 or 3

Answer 9

3 and 4
just by looking at it

why? -- b/c

3 * 4 =12
and
3+ 4 = - (-7)

Answer 10

im gonna use the most complicated method i know, the quadratic formula......
-b+or- radicle b^2 - 4ac all over 2a.........

working it out......

working it out......

working it out......

got it!!!!!

the answer is......

x=either 4 or 3





Ps. people above me, its not a coordinate! its a solution set!
u dont write it (4,3) or (3,4)..... u write it S={4,3} or S={3,4}





u just got served! mathematically speaking.