How to so this equation?

Question

I need to know how to do this equation along with showing the work so that I understand it and dont just know the answer.
72-22x+x2 the 2 is to the second power im just unable to write it correctly. thanks!

Answer 1

What you have given is an expression it is not an equation. When you equate the expression to zero it becomes an equation. And only equations can be solved. Now your equation can be re-written as x^2-22x+72 = 0.
Now factorise, x^2 - 18x - 4x + 72 = 0
That is x(x-18) - 4(x-18) = 0
Or (x-4)(x-18) = 0
Therefore, x = 4 and 18

Answer 2

This is a quadratic equation which will result in two answers.

write the terms in decreasing order of powers

x^2 - 22x + 72
Lets solve it using the middle term split method.

What you have to do is, get two numbers, which add up to the middle term(-22x) and when multiplied with each other, get the third term(72)

to do this, let us find the factors of 72
the factors will be 2,2,2,3,3(i hope you know how to get factors)
using these, lets take 18(3*3*2) and 4(2*2)

now, when you add the numbers, you get 22 and when multipled, you get 72 which is what we want.

now write these two numbers in place of the single middle term

x^2 - 4x - 18x + 72
take x common from the first two numbers and 18 common from the last two

you get,
x(x - 4) - 18(x - 4) [it is necessary that the term in the brackets must be the same for both]

simplifying, (x-18)(x-4)
equate this to 0
x-18 = 0 and x-4 = 0

thus , x = 18 or 4.

Answer 3

You first write the equation in ax^2 + bx + c format

x^2 - 22x + 72

(x- )(x- )

Now you look for factors of 72 (since it is positive 72, but 22 is negative, the two factors need to be negative because (- + - = -), but (- * - = +). They add to 22 and multiply to 72)

1, 72
2, 36
3, 24
4, 18...this is the set we are looking for
6, 12
8, 9

so the solution is (x-4)(x-18)

Answer 4

72 - 22x + x^2

I'm assuming it's equal to 0 and you're looking to solve for x. In which case, rearrange everything so the larger powers are first. In other words:

x^2 - 22x + 72

From here, take the coefficients (the numbers in front of the x) and set them equal to the following variables:

a = 1
b = -22
c = 72

From here, use the quadratic formula to solve for x:

x = ( -b +- sqrt( b^2 - 4ac ) ) / 2a
x = ( -(-22) +- sqrt( (-22)^2 - 4(1)(72) ) ) / 2(1)
x = ( 22 +- sqrt( 484 - 288 ) ) / 2
x = ( 22 +- sqrt( 196 ) ) / 2
x = ( 22 +- 14 ) / 2
x = 11 +- 7

So that means that:
x = 18
x = 4

Answer 5

well, you have to factor the equation. rewrite it so that the powers go in order : x2 -22x+72. find the possible numbers that multiply to =+72, but add up to +-22. so, when you break it down, you get (x-18)(x-4). if you foil this to check your work, you get x2 -18x-4x+72=x2-22x+72. i hope this helps!

Answer 6

You just need to factor it. First, you may want to rewrite the equation into the form that you're probably used to seeing it. In other words, re-arrange the terms in order of decreasing powers:

x² - 22x + 72

Now you just factor as you normally would...

-18 * -4 = 72 and -18 + -4 = 22

So...
(x - 18) (x - 4)

If there is anything about my explanation that you don't understand, feel free to send me an e-mail and I'll try to clarify any confusing parts. :)

Hope it helped!

Answer 7

x^2-22x+72
(x-4)(x-18)

x=4 x=18

Answer 8

72-22x+x^2

This becomes...

x^2 - 22x + 72

This becomes...

(x-a)(x-b) <= We know this, because -22x must ADD to -22

Thus, what are a & b?

Simply find out what multiplies to 72 and adds to -22,

a+b = -22
a * b = 72

Since b = 72 / a you find that...

a + 72/a = -22 so...

a^2 + 72 = -22a

a^2 + 22a + 72 = 0

and you can then use the quadratic formula to find a, then to find b.

Answer 9

ok I haven't done this for a while so I'm not sure but i'll try to help you
1.) 72-22x-x2
-x -x
--------------------
72 -22 x

2.) x=50 or 50x

Answer 10

1st of all.. move it around so it looks like
(x^2)-22x+72
then simply factor it into
(x-4)(x-18)
then your answers are
x=4 and x=18