Please i need to pass math this year

Question

Can somebody please show me how you do this problems

When you have a trinomial:find the x

Factoring

5 2x^2 -4x-6=0

Completing the square

6 2x^2-4x+3=9

Quadratic formula

7 2x^2-4x=6

Answer 1

2x^2 -4x -6 = 2(x^2-2x-3) = 2(x-3)(x+1)

2x^2-4x+3=9

2(x^2-2x +1) =9-3+2(1)

2(x-1)^2 = 8

(x-1)^2 =4

x-1= + or- sqr4

x=1+ or - 2 = -1 or 3

2x^2 -4x = 6

2x^2 -4x -6 =0

x = 4/4 + or - (1/4)sqr(16+4(2)(6)) = 1+or -2 = 3 or -1

Answer 2

1) 2x²-4x-6 = 0

First we want to find factors of the coefficient in front of x². In this case, 2 only has two factors, 1 and 2.

(2x ) (1x )

Anytime we have a coefficient of 1, we don't need to write it down as x is the same as 1 x.

(2x ) (x )

Next, we look at the sign of the constant, in this case it is negative. The only way to have two factors multiply to give you -6 is if one of them is positive and one of them is negative.

As a result, we have two possibilities of where the signs go.

(2x - ) (x + )

(2x + )(x - )

Next, we want to find the factors of the constant, 6. In this case, 6 has the factors of (1,6) and (2,3). At this point, we need to guess and check. The way we do this is by literally guessing different combinations of the factors and checking if it factors out to the original trinomial. To make your life easier, you only need to check if the coefficient of x ends up being -4.

(2x - 1) (x + 6) WRONG, coefficient of x is 11

(2x + 1)(x - 6) WRONG, coefficient of x is -11

(2x - 6) (x + 1 ) CORRECT, coefficient of x is -4

Now that we have correctly factored the expression, we have to remember that this expression was equal to zero. This is how we solve for x.

(2x-6)(x+1) = 0

Anything multiplied by 0 will be equal to 0, so we know that if x + 1 = 0, then the whole expression has to be equal to zero. Furthermore, if 2x-6 = 0, then the whole expression is also equal to zero.

2x-6 = 0

2x = 6

x=3

x+1 = 0

x= -1

Thus, x has two solutions, x=3 and x=-1.

Factoring is a skill that takes a lot of practice to master. I highly recommend doing many problems like this to get better at guessing and checking. It can be very tedious checking through many combinations and with practice, you will be able to filter out combinations and save yourself a ton of time.

Answer 3

Answer for Factoring 2x^2 -4x-6=0

take out a common factor 2

=2(x2-2x−3)

=2(x-3)(x+1)

Answer for Completing the square 2x^2-4x+3=9

Given that, 2x^2−4x−6=0.

∴2x^2−4x=6.

To complete the square on L.H.S., we need

Last Term =(Middle Term)²/4×First Term=(−4x)²/4⋅2x²

= 16x²/8x²

= 2

Adding 2 on both sides,

2x²−4x+2=6+2

∴2(x²−2x+1)=8

∴2(x−1)²=8

∴(x−1)²=4

∴(x−1)=±√4

∴x=1± 2, is the desired soln.

we get the soln. set ={3,−1}.

Answer for Quadratic formula 2x^2-4x=6

The Quadratic formula is ax²+bx+c=0, the values of x (factors) which are the solutions of the equation are given by:

x=b±√4⋅a⋅c / 2⋅a

Here, a=2, b=-4 and c=-6, so

x=-4±√4⋅2⋅(−6) / 2⋅2

x=(-4±√−48 / 4)