maths easy help?

Question

3x^2+5x-12=0
factorize please and say why u did wat
im doin somthing wrong thnx
i need two possible values of x i think

Answer 1

3x^2 + 5x - 12 = 0
3x^2 + (9x - 4x) - 12 = 0
(3x^2 + 9x) - (4x + 12) = 0
3x(x + 3) - 4(x + 3) = 0
(x + 3)(3x - 4) = 0

x = -3
x = 4/3
****************
If you can't see a way to factor it, you can always use quadratic formula:
a = 3
b = 5
c = -12

x = [-b +- sqrt (b^2 - 4ac)] / 2a
= [-5 +- sqrt (5^2 - 4(3)(-12))] / 2(3)
= [-5 +- sqrt (25 + 144)] / 6
= [-5 +- sqrt (169)] / 6
= (-5 +- 13) / 6
= -18/6 AND 8/6
= -3 AND 4/3

Answer 2

3x² + 5x - 12 = 0

The middle term is + 5x

Find the sum of the middle term

Multiply the first term 3 times the last term 12 equals 36 and factor.

Factors of 36

1 x 36
2 x 18
3 x 12
4 x 9 . .←. .use these factors
6 x 6

+ 9 and - 4 satisfy the sum of the middle term

insert + 9x and - 4x into the equation

3x² + 5X - 12 = 0

3x² + 9x - 4x - 12 = 0

3x(x + 3) - 4(x + 3) = 0

(3x - 4)(x + 3) = 0

- - - - - -

Roots

3x - 4 = 0

3x - 4 + 4 = 0 + 4

3x = 4

3x / 3 = 4 / 3

x = 4 / 3

- - - - - - - -

Roots

x + 3 = 0

x + 3 - 3 = 0 - 3

x = - 3

- - - - - - - - -

The two values of x

x = 4/3

x = - 3

- - - - - - -s-

Answer 3

Let the factors be (ax + b)(cx + d).
Then ac = 3, giving possibilities:
a: 1 3
c: 3 1

bd = -12, giving possibilities:
b: -12 -6 -4 -1 -2 -3
d: 1 2 3 12 6 4
except that the signs may need switching.

Now look for pairs such that bc + ad = 5.
a = 3, c = 1, b = -4, d = 3 looks good, and gives the right sign for the x term.

The factors are therefore:
(3x - 4)(x + 3).

If bc + ad had come to -5, then you would have needed to switch the signs of b and d.

Answer 4

I use the good old formula x=(-b (+/-) sqrt(b^2-4ac)) / 2a

so in this case x = (-5 + sqrt(25+144))/6
and the other value of x is x = (-5 - sqrt(25+144))/6

first value
x = (-5 + sqrt(169))/6
= (-5 + 13)/6
= 4/3

other value
x = (-5 - sqrt(169))/6
= (-5-13)/6
= -18/6
= -3

so we can use x= 4/3 and x=-3 to get the factors:

(x+3)(x-4/3)

Answer 5

First you factorize (x+3)(3x-4)=0
then you can solve x by:
x+3=0
x=-3
or
3x-4=0
3x=4
x=4/3
x is -3 or 4/3

Answer 6

x(3x+5)=12

Answer 7

3x^2+5x-12=0
x=(-5+sqrt(25+144))/6
x=-3,4/3.