Question

2x2-x-6 = 0
What is one solution to the equation?

Answer 1

X=2

Explanation:

Easy, easy!

Let's use trial and error!

Since we can factor this equation, let's do it!

`2x^(2) -x-6=0\\2x^(2) -x=6\\x(2x-1)=6\\\\`

So this means that we have 2 factors: x and (2x-1)

Those 2 factors multiplied by each must other equal 6.

So at the top of my head two numbers that multiplied by each other equal 6 are 3 and 2.

Let's try x=3 and (2x-1)=2

Since x=3,

`(2x-1)=2\\(2(3)-1)=2\\(6-1)=2\\(5)\\eq 2`

It means that we should keep trying!!!

Let's try x=2 and (2x-1)=3

Since x=2,

`(2x-1)=3\\(2(2)-1)=3\\(4-1)=3\\3=3`

So we have our answer!!!

x=2

Answer 2

x1=2 and x2 =-3/2

Explanation:

2x^2-x-6=0 (quvadratic equation)

a=2, b=-1, c=-6

x1=(-b+sqrt(b^2-4ac))/2a

x1=(-(-1)+sqrt((-1)^2 - 4*2*(-6)))/2*2

x1 =(1+sqrt (1+48))/4

x1= (1+sqrt(49))/4

x1 =(1+7)/4

x1=8/4

x1=2

x2=(-b-sqrt(b^2-4ac))/2a

x2=(1-7)/4

x2=-6/4

x2=-3/2