I need some assistance with this problem: 2x²+4x-30=0?

First, divide everything by 2 to get x²+2x-15=0
that will make it a lot easier

NO, NO, NO!!! 2x²+4x-30=0 can NOT work with (2x+?) (2x+?). The 2x² can be simplified into (2x+?) (x+?). (2x²=x and 2x)
ALGEBRA I WAY:
simplify to 2(x²+2x-15)=0
either guess and check, or use the way given below to find the rest. 2(x+5)(x-3)=0 solve for x in both parenthesis:
x+5=0 x=-5
x-3=0 x=3
plug either of these numbers into any of the equation and it will work

ALGEBRA II WAY:
To find the other two, use these equations:
sum= -b/a. meaning the sum of the roots is -b/a.
product= c/a. meaning the product of the roots is c/a
a= the number in front of the variable with the exponent(2x²), or 2 in this case
b= the number in front of the variable with no exponent (4x), or 4 in this case
c= the number with no variable (-30), or -30 in this case

so the sum of the roots is -4/2, or -2
and the product is -30/2, or -15
you are looking for two numbers that are -2 added and -15 multiplied. (-5 and 3)

The roots, if you don't know, are what the x's are equal to. In order for this equation to work, x would have to be the opposite of whatever else is in the ( ), in order to cancel out and equal zero.
Knowing this, the roots are 3 and -5. So x=-5, or x=3

QUADRATIC EQUATION:
x=(-b(+-)(b²-4ac))/2a

I AM GLAD THAT I'M WELCOMED HERE, MISTER, AND YOU BETTER GIVE ME THE BEST ANSWER. PAY ATTENTION IN CLASS, MISTER. GOOD DAY TO YOU.
STUDY THIS FOR A WHILE, AND YOU WILL BECOME AN EXPERT

First off, you've got an incorrect assumption here : 2x times 2x doesn't equal 2x^2, it equals 4x^2. So your factoring should really start like this :

( 2x___ ) ( x___ )

Now let's try to find the right values.

2x^2 + 4x - 30 = 0

To get 30, we need to multiply two numbers together. The possible pairs are 1 and 30, 2 and 15, 3 and 10, 5 and 6. Because it's -30, one of the two numbers must be negative.

These two numbers also have to be able to add up to 4 but remember, one of them is going to get multiplied by 2 before adding. A quick guess shows that if we use 5 and 6 with the 5 being multiplied by 2 to make 10, these numbers will be 4 apart. So :

( 2x__6 ) ( x__5 )

But what should the signs be? Since we want the 4 in the middle to be positive, our larger number in the addition needs to be positive. In this case, the 10 from multiplying 2 by 5.

( 2x - 6 ) ( x + 5 )

You can check this with FOIL, which means multiply First, Outer, Inner, Last.

Firsts : 2x times x = 2x^2
Outers : 2x times 5 = 10x
Inners : -6 times x = -6x
Lasts : -6 times 5 = -30

So :
2x^2 + 10x - 6x - 30
2x^2 + 4x - 30 [Yay, it worked!]

So now set both sides to zero.

2x - 6 = 0
2x = 6
x = 3

x + 5 = 0
x = -5

And there are your two solutions. Hope this helped.

2x² + 4x - 30 = 0
x² + 2x - 15 = 0
x² + 2x =15

Completing the square: Divide coefficient of the x term by 2
and square the quotient: (2/2)² = 1²
Add to both sides of the equation:
x² + 2x + 1² =15 + 1²
(x + 1)² = 16
x + 1 = ± √16
x = -1 ± √16
x = -1 ± 4

x₊ = -1 + 4 = 3
x₋ = -1 - 4 = -5

2x²+4x-30=0

it actually factors into

(2x + ?) (x + ?) = 0

So....

to make the outside products equal -30, you know there is a - and a +

So (2x + ?) (x - ?) = 0

The numbers that fit are -5 and 6, -6 & 5, -10 & 3, and -3 & 10

Try those numbers and you'll figure out that

(2x - 6)(x + 5) = 0

This is a quadratic equation: ax² + bx + c = 0 and is normally solved using the quadratic formula x = -b + or - sqrt(b² - 4ac)/2a which will give you x=0 and x = -8.

While you can factor the problem your initial (2x + ?) (2x +?) is wrong because once you FOIL the problem you would get 4x² right off the bat and the equation clearly shows 2x². My solution to the factoring aspect is (2x - 6) (x + 5) because when you foil the problem out you get the following:

2x * x = 2x²

-6 * x = -6x

2x * 5 = 10x

-6 * 5 = -30

-6x + 10x = 4x

First of all, 2x *2x is not 2x^2 it would be 4x^2. So that was wrong. And your operators are wrong because with two plus' you can't get -30. Because you have a positive 4x and a -30 you have to have a + and a -. I dont know how to explain this part just put the + in the first bracket and the - in the second one. Now just find the factors of 30 and plug them in for the ?'s. Then just distribute the numbers and you have the awnser. Finally here is the awnser hoped this helped you out. (You get 2 numbers with x, just put them together.)

Awnser: (2x+10)(x-3)

2x2+4x-30=0
2(x2+2x-15)=0...make coefficent of x 1
x2-3x+5x-15=0
What are the factors of 15? 3 and 5, hence the reason they were used
x(x-3)+5(x-3)=0
factorize
(x+5)(x-3)=0
x=-5 and x=3
sorry i couldnt get the exponent 2 so i typed it like this.hope u understood

You have given a wrong factorization.

The factor of the equation is:

2x²+4x-30=0 -----> (2x - 6) (x + 5) = 0

FYI, you CAN'T break down 2x² into 2x and 2x becuase if you're going to multiple 2x by 2x, the answer is 4x², and it is not equal to 2x².

this is called a magic number problem, since there is a value in front of the x^2, which is 2. what you do is you take that 2, and multiply it by the number at the very end, which is -30, to make it -60. then, as you said, you set it up like (2x + ?)(2x - ?).

what you want to find is the numbers that add to be +4 and multiply to be -60. they are 10 and -6. so now it looks like this.

(2x-6)(2x+10)

then you can simplify by GCF. with both parts of the problem, a 2 can be divided out. so then you have

(x-3)(x+5)

then you set each part equal to 0, and solve for x. when you do that, x= +3 and -5. hope that helped

best answer?