Math geniuses needed please can you help me with the following quadratic equation x^2-2x-63=0 how do I do this

Question

here is the question again
x^2-2x-63=0

I think it is supposed to go something like this the only problem I am not sure if I put the negative and positive signs on the right side

x^2-2x-63=0
(x 9)(x 7)
as you can see i left out the positive and negative signs because I am not sure how to do that part:(

x 9=0 x 7=0
the positive and negative signs are not in this as well

then we bring the 9 over and 7 over then it should look something like this
x= 9 x= 7

need pos or neg signs
then right a solution set



your help is muchly appreciated:)

Answer 1

x^2 - 2x - 63 = 0

First multiply the first and last terms to get -63x^2

Then, split the 'x term' into two parts that have a product of -63x^2 and a sum of -2x

x^2 - 9x + 7x - 63 = 0

Factor two groups

x(x - 9) + 7(x - 9) = 0

Divide out the common factor of (x - 9)

(x + 7)(x - 9) = 0

Set factors equal to zero and solve

x + 7 = 0
x = -7

x - 9 = 0
x = 9

The solutions are -7 and 9

{ -7, 9 }

Answer 2

Look at the sign of the last number. It's negative 63, coming from a product of 9 and 7 with opposite signs, as you said.
Next look at the middle sign. It's negative, so the larger number (9) gets that sign.
So, (x-9)(x+7)= 0
You can use F.O.I.L. to check, and I think you'll see how this always works from combining like terms.
X^2 -9x +7x -63 = 0, combine like terms and you get the original problem back.
Now, if the product of two numbers is zero, one of them HAS to be zero.
So if x-9 = 0, then x would be 9.
But if x+7 = 0 then x would be -7.
Therefore x is 9 or -7, and you can check that back in your original equation.
(9)^2 - (2)(9) - 63 = ?
81 - 18 - 63 = 0, so it checks.
(-7)^2 -(2)(-7) - 63 = ?
49 - 14 - 63 = 0.

Answer 3

You have to consider the -2x part as well as the sign before the '63' to determine signs. For example, when multiplying + and - you get the folllowing (+)(+)=(+), (-)(-)=(+), and (-)(+)=(-)

In this case, you have a -63, so the only possibility is (-)(+)=(-)
Now look at the -2x. you need 9 and 7 to be added to equal -2. Therefore, since we need a -2, then the 9 will be negative and the 7 positive giving us -9+7= -2 then solve for a solution set as you have already started.

Answer 4

x^2-2x-63
lets suppose that the root is m and n so
(x+m)(x+n)=x^2-2x-63
so m x n have to equal -63, the result of multiplication is negative,
therefore one number have to be negative and the other is positive,
m+n have to equal -2, the result of addition is negative,
therefore the negative number must be greater than the positive one.
so take (x-9)(x+7)=0
(x-9)=0 , (x+7)=0
x={ 9 , -7 }

Answer 5

Hello

The two numbers have to multiply to be -63 and add to be -2 so we need -9 and +7 giving us

(x-9)(x+7) = 0

now that means that x-9 = 0 and x + 7 = 0 so we get

x=9 or x = -7.

Now put thes in to check our original eqaution.

(-7)^2 - 2*(-7) -63 = 0

and
9^2 - 2*9 -63 = 0

Hope This Helps!!

Answer 6

You are definitely on the right track, good job so far! You know about FOIL, right? Well, in order to see what the signs should be, just do the O and the I (outer and inner multiplication). You get 9x and 7x and those are together supposed to make -2x. So which would be positive and which would be negative to make -2x? Based on the rules of adding negatives and positives, the result takes the sign of the larger number, so 9 must be negative to make -2x.

Answer 7

The positive and negative sign choice is not all that tough, and you should get some help if you are hung up on it. The rule is simple, if the x-term is positive, the larger integer gets the plus sign, and vice versa. Then we have (x-9)(x+7)=0 as our factoring [that's the vice versa part of the rule]. The RULES say that both of these factors are set to zero to find the roots, from which we wind up with x=-7 and +9. I suppose your teacher likes to express this as x= { -7,9 } to be "fancy-shmansy"

Answer 8

It would factor out like this:

(x-9)(x+7). Therefore x-9=0 and x+7=0.

Solving for x, you get x = 9 and x = -7

Answer 9

Well since the coefficient of x is negative you should put the negative sign infront of the bigger number.

(x-9)(x+7)=0 so

x=9 or x=-7

x= {-7,9}

Answer 10

x+9 x-7