Please help me with this math problem?

Question

Solve the following equation by factoring : x^2 -5x-14=0
The unit we have been covering is over Quadratic Equations and parabolas just in case you need to know. Thank you in advance. I am math challenged. Oh, and please try to explain each step as thouroughly as possibe.

Answer 1

Basically what it is asking you for is to factor it out. To do so you need to find two numbers that multiply to -14, and add to -5. These two numbers would be -7 and 2.

That means you would factor it as such:
(x-7)(x+2)=0

There are two solutions:
x=7, and x=-2

Answer 2

You need two factors such that
(x + a)(x + b) = x^2 -5x -14
x^2 + ax +bx + ab = x^2 -5x -14
x^2 + (a +b)x + ab = x^2 -5x -14, so
ab = -14, and
a + b = -5
a or b must be negative, but not both.
14 has only 4 integer factors, 1,2,7, and 14.
Listing the possible solutions, you have
14 - 1 = 13
7 - 2 = 5
2 - 7 = -5, so you need look no further.
Your factors are
(x + 2)(x - 7)

Answer 3

the quadratic formula states that -b +/- (the square root of b^2 - 4ac) all divided by 2a is equal to x. In this case, a= 1 because there is no coefficient in front of x^2, b= -5 (from -5x) and c= -14. So using the formula

x= 5 +/- (the square root of) 25- -56 all divided by 2

x= 5 +/- (the square root of) 81 all divided by 2

x= 5 +/- 9 all divided by 2

x= 5 + 9 divided by 2 = 7 AND x= 5-9 divided by 2= -2

Answer 4

First since x is squared then it breaks into 2 x's. And because the 14 at then end is a negative then one number will be positive and the other will be negative.
(x+__ )(x-__). Now, what numbers multiply to get negative 14 and add together to get negative 5. That would be positive 2 and negative 7
(x+2)(x-7)

Answer 5

x^2 -5x-14= 0
factorization method
x^2-2x-7x-14=0
=>x(x-2)-7(x-2)=0
=>(x-2)(x-7)=0
=>(x-2)=0 ; (x-7)=0
=>x=2 ; x=7
x=2,7

Answer 6

(x-7)(x+2)
x= 7,-2