help!! plz I am desperate!! what is x2 + 4x = 21?

Question

I have been doing this one question for like 3 hours and cant get it plz plz plz help!!

Answer 1

do you mean x^2 + 4x = 21?

what is asked in that problem? are you ask to factor out that equation or you are to find for the value of x?


well to factor out this equation: observe the steps bellow

*factoring trinomial in the form x^2 + bx + c

x^2 + 4x = 21

x^2 + 4x - 21 = 0

(x + ___) (x + ___)

now, think of 2 factors of 21 that when you add it or subtract it you'll get 4, w/c is the constant of the middle term of x^2 + 4x - 21.

factors of 21:

1 and 21

1 + 21 = 22
1 - 21 = -20
21 - 1 = 20

3 and 7

3 + 7 = 10
3 - 7 = -4
7 - 3 = 4

so the possible factors of 21 that can fill the blanks of (x + ___) (x + ___) are 3 and 7.

so the answer is ( x + 3) (x - 7)

*check it by multiplying a binomial by a binomial

if you're trying to find for the value of x do what we did earlier (factor out the equation) then the next step is as follows:

( x + 3) (x - 7) = 0

x + 3 = 0 x - 7 = 0
x = -3 x = 7

the values/solutions/ for x are -3 and 7.

Answer 2

x^2 + 4x = 21

First, move everything to the left hand side.

x^2 + 4x - 21 = 0

Now, look carefully at the middle term which is the coefficient of x (i.e. 4) and the third term which has no x (which is -21).

(x + ?) (x + ?) = 0

Here's where you ask yourself: What two numbers add up to make 4, and multiply to make -21? The answer to that question is +7 and -3. Note that 7 + (-3) = 4 (the middle term) and 7(-3) = 21 (the third term). In the question marks, put +7 and -3.

(x + 7)(x - 3) = 0

Equate each factor to 0, and you have your solutions.

x + 7 = 0, so x = -7
x - 3 = 0, so x = 3

Therefore,

x = {-7, 3}

That's the key trick to these questions; recognizing what two numbers add up to make the middle term, and what two numbers multiply to make the third term. Here's another example to help you out.

EXAMPLE: x^2 = 8x + 20

Again, move everything to the left hand side.

x^2 - 8x - 20 = 0

What two numbers add up to make -8 and multiply to make -20? The answer is -10 and +2, so this factors as

(x - 10)(x + 2) = 0

Therefore,
x - 10 = 0
x + 2 = 0

So
x = {10, -2}

Answer 3

x² + 4x - 21 = 0
(x + 7).(x - 3) = 0
x = - 7 , x = 3
Tip: Don`t spend such a long time on a question such as this.Call a halt and go back to it later or get help. Good luck!

Answer 4

x2 + 4x = 21
x2 + 4x - 21 = 0

use reverse foil to make:

(x - 3) (x+7)

x - 3 = 0
x= 3

x + 7 = 0
x = -7

so x = 3, -7

Answer 5

x^2 + 4x = 21

turn into a quadratic
x^2 + 4X -21 = 0

solve using quadratic formula AX2 + BX + C = 0
gives:

x = 3
x = -7

Answer 6

x= -7 and x=3

x2+4x-21=0
(x+7)(x-3)=0
x= -7 and 3

Answer 7

6x=21 divide that by 6 and you will have your answer which is a whole number and a fraction. I can't give you the answer but I am helping you on that. I don't do someone else's homework though.