How do I solve this. I assume I use the quadratic formula..but how??

Question

x^2 + 4X > 21
How would I solve this? Please explain. Thanks.

Answer 1

well...first subtract 21 from both sides so you can set it to 0...

you have x^2 + 4x -21 = 0

then think of all multiples of 21...(21, 0) (3, 7)...
of your options which two can somehow add/subtract to equal 4 (4x)
since it is -21 you know the signs of your quadratic equation are going to be different (one positive, one negative)

since 7 and 3 can create 4, you know its going to be either (x+7)(x-3) or (x-7)(x+3)

since its +4x, you know the 7 has to be positive which will give you (x+7)(x-3)

make sense? :)

Answer 2

No need to use the Qaudratic Formula, this is pretty simple. This is what I do:

1- put the 21 on the left side so the rite side is 0:

x^2 +4x - 21 = 0

2- Now, we look at the 4X and the -21 and we need two multiples that give -21 which also when added, give 4. The two numbers would be 7 and -3, since 7 x -3 = -21 and 7 - 3 = 4.

2- Now that we know those two integers, all you gata do is put em into the brakets like this:

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

3- Now all you need to do is draw this graph. You know that the x intercepts are -7 and 3 and then plot it. After that shade the region less than zero and you're done.

Answer 3

The answer from G is correct

Geometrically a quadratic inequality be be a portion of the number line (ie x axis) and it will fall into 1 of 3 classes
1. No solution as the quadratic does not intersect the x axis
2. The "inner" part of the quadratic. Using this example this would be -7 < x < 3. This is not the correct answer in this case.
3. the two "outer parts" of the quadratic. This would be (in this case) x < -7 or x > 3. This is the correct answer.

Alternatvely you could display the naswer using a number line.

Answer 4

x^2 + 4x > 21
x^2 + 4x -21 > 0
(x + 7)(x-3) > 0
x > -7 and x > 3
x > 3
since x must be greater than 3, you obviously don't need to say that x must be greater than -7. So the answer is just x > 3

MY ANSWER is PERFECT and Simple. Just read my answer and ignore what everyone else said.

Answer 5

x^2+4x-21>0
you factor it and you will get:
(x+7)(x-3)>0
because the product is greater than 0 so the (x+7) and (x-3) have to have the same sign.

(x+7)>0 and x-3>0
x>-7 and x>3 therefore x>3

or
x+7<0 and x-3<0
x<-7 and x<3 therefore x<-7

the answer is x<-7 or x>3