Question

Solving Quadratic Equations by Factoring

Answer 1

Answer:

x=-7      x=2

Step-by-step explanation:

x^2+5x-14=0

Factor

What 2 numbers multiply to -14 and add to 5

7*-2 = 14

7 -2 =5

(x+7) (x-2) = 0

Using the zero product property

x+7 = 0   x-2 =0

x=-7      x=2

Answer 2

Answer:
x=(2,-7)

Instruction:

I struggled with factoring too, it’s not easy to learn, but there are a few tricks i know that make factoring equations with a 2 power very simple!

Before you begin factoring, the equation must be equal to zero.

The first trick:

Write down “ (x )(x ) = 0 .” This is the outline for your answer.

The second trick:

In equations like these, there are always going to be some combination of two plus or minus symbols. The most important one is the second. If the second sign is a plus sign, the equations will have the same sign as the first sign in the equation. If the second sign is a minus sign, then the signs in the new equation will be different.

(x - )(x + ) = 0

The third trick is to find the numbers that are subtracted from x. These numbers are positive or negative based on the sign in the equation next to their placement, and are a multiple of the y-intercept value (the 3rd number, -14). The sum of these numbers must be equal to the slope (positive 5)
In this case, the sum of -2 and +7 is equal to the slope, and the product of these numbers is -14. Fill these in respectively.

(x - 2 )(x + 7 ) = 0

Now we can infer the answers from here. The solutions to this equation are equal to the opposite of the numbers.

The opposite of -2 is +2, or just 2, and the opposite of 7 is -7.

x = (2,-7)

This can be checked by plugging in the numbers to the last equation. Lets check 2 first.

((2) -2)(x+7)=0
(0)(x+7)=0
0=0
2 is correct.

(x-2)((-7)+7)=0
(x-2)(0)=0
0=0
7 is correct.

I have know proven my answer to be correct! Have a nice day

-Blake :)