how i do solve this: x^2+2x-24=0 i need to show work too?

Answer 1

you may split the middle term

x²-4x+6x-24=0

x(x-4)+6(x-4)=0

(x+6)(x-4)=0

so, x=4, -6

or you may use the quadratic formula

Answer 2

k so this is a quadratic equation and there are two possible answers to it. I am solving it by factoring:

x^2 + 2x - 24 = 0 (here u have to find two numbers that multiply to -24 and add up to 2, those numbers are +6 and -4)
x^2 + 6x - 4x - 24 = 0 (so i divided the 2x into 6x - 4x)
x(x + 6) - 4(x + 6) = 0 (factoring out x and 4)
(x + 6)(x - 4) = 0
x + 6 = 0 or x - 4 = 0
x = -6 x = 4

Answer 3

Hopefully you have learned the quadratic formula. This states that if ax^2 + bx + c = 0 then x = [-b +/- the sqrt root of (b^2-4ac)] / 2a.
Applying this formula, a = 1, b = 2, and c = -24.
Thus x = [-2 +/- the sqrt of (4+96)] / 2.
So x = [-2 +/- 10]/2 and there are two answers:
x = [-2+10]/2 = 4 and x = [-2-10]/2 = -6.
Another way of solving this is to factor the given quadratic into (x-4)(x+6)=0
(check this factorization by foiling (x-4)(x+6)).
This can only be true if either x-4=0 or x+6=0, this is the same as saying x=4 or x=-6. Voila!

Answer 4

I saw many answerers using the formula of the 2nd order equation, i see that there is NO NEED for using it

Here the equation is so simple, so it can be solved by direct factorization

x^2 + 2x - 24 = 0

( x + 6 ) ( x - 4 ) = 0

x = -6 OR x = 4

Answer 5

first thing you should do in these types of problems is know how to solve them

you first need to split the middle term into two values , say , m and n

therefore , the rule goes that m+n= middle term and m x n = the product of the terminal terms

in your equation first factorize the third term: 24 = 2 x 2 x 2 x 3

2 x 2 = 4
2 x 3 = 6

also 6 - 4 = 2 which is the second term . hence m=6 and n= -4

your equayion will look like:

x^2 + 6x - 4x -24 =0
x(x +6) -4(x + 6) =0
(x - 4)(x + 6) = 0

hence x=4 or x = -6

Answer 6

We solve this by factorisation:

x^2 + 2x - 24 = 0
x^2 + 6x - 4x - 24 = 0
x(x + 6) - 4(x + 6) = 0
(x + 6)(x - 4) = 0

Either x + 6 = 0 (or) x - 4 = 0
x = -6, 4

Answer 7

First we need to find out what multiplies to get -24. So you have 1, -24; -1, 24; -2, 12; 2, -12; 4, -6, and 6, -4. Also, the two numbers must add up to be 2 so it has to be 6 and -4. So your answer would be (x+6) (x-4) so x = -6 and x = 4

Answer 8

The given equation is of the form :ax^2+bx+c =0 where a= 1 , b=2 & c= -24 .
The roots of quadratic equation like this is given by a formula :

x = (-b +/- square-root of ( b^2 - 4ac))/ 2a

Therefore we have
x = ( -2 +/- square-root of (2^2 - 4(1)(-24)))/ 2(1)
since a =1 , b = +2 & c = -24

x = (-2 +/- square-root of ( 4 - 4(-24)))/ 2

x = ( -2 +/- square-root of ( 4 + 96))/ 2

since (-4)(-24) = +96

x = ( -2 +/- square-root of (100)) / 2

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

since square-root of 100 = 10

x = ( -2 + 10 ) / 2 and x = ( -2 - 10) / 2

x = + 8 / 2 and x = -12 / 2

x = 4 and x = -6 (Answers)

Answer 9

x^2 + 2x - 24 = 0

x^2 + 6x - 4x - 24 = 0

x (x + 6) - 4 (x + 6) = 0

Taking (x + 6) out from both terms:

(x + 6) (x - 4) = 0

Therefore,
either : x + 6 = 0 or: x - 4 = 0
either: x = -6 or: x = 4

Answer 10

x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
x + 6 = 0 or x - 4 = 0
x = -6 or x = 4

Answer 11

This is a quadratic equation. You solve it by factoring the left hand side: (x+6)(x-4)=0. Then set each factor equal to zero and solve the equation. x+6=0, therefore x=-6 is one solution. Also, x-4=0. Therefore x=4 is another solution.