Question

Use the X method to find the solutions of

6x2 + 2x – 20 = 0.

x =

x =

Answer 1

`x=-2`,
`x=(5)/(3)`

Explanation:

`6x^2 + 2x - 20 = 0`

In the given equation all terms are divisible by 2.

`3x^2 + x - 10 = 0`

Product is 3 times -10 = -30 and sum is 1

-5 times 6 is -30

-5+6 is 1, factors are -5 and 6

Break the middle term using the factors

`3x^2-5x+6x - 10 = 0`

Group first two terms and last two terms

`(3x^2-5x)+(6x - 10) = 0`

Factor out GCF from each group

`x(3x-5)+2(3x - 5) = 0`

Factor out 3x-5

`(x+2)(3x-5)= 0`

Set each factor =0 and solve for x

`x+2=0 , x=-2`

`3x-5=0, 3x=5`

`x=(5)/(3)`

Answer 2

The solution to the quadratic equation given by:
6x^2+2x-20=0
will be:
6x^2+2x-20=0
factoring the above we get:
6x^2+12x-10x-20=0
6x(x+2)-10(x+2)=0
(6x-10)(x+2)=0
hence:
6x=10
x=10/6=5/3
or
x+2=0
x=-2
Thus the answer is:
x=5/3
x=-2