what are two numbers that multiply to equal -35 but add to equal +2

Answer 1

Let's call the 2 numbers "x" and "y".

1. x * y = -35
2. x + y = 2

Rearrange equation 2:

x = 2 - y

Substitute into equation 1:

(2 - y) * y = -35

Solve (first distribute):

2y - y² = -35

y² - 2y -35 = 0

(y - 7)(y + 5) = 0

y = 7 y = -5

Sole for "x" using either equation (I'll use #2):

When y = 7 --> x + 7 = 2

x = -5

When y = -5 --> x +(-5) = 2

x = 7

The answer is -5 and 7

Answer 2

Hi Shayle!

In this problem, we have to find two numbers (let's say they are x and y) that follow these conditions. So let's write it out.

x * y = -35

x + y = 2

Now let's solve for y in the second equation

x + y = 2

y = 2 - x

Now that we solved for y, let's plug that into our first equation

x * y = -35

x * (2 - x) = -35

2x - x^2 = -35

x^2 - 2x - 35 = 0

(x-7)(x+5) = 0

x = 7 or x = -5

Now we have two possible values for x, let's check them back into our other equation

7 + y = 2

y = -5

-5 + y = 2

y = 7

Here, we have one set of numbers where they follow the given parameters (it's reversed which is why it shows as two sets)

(7 , -5)

Answer 3

Given a*b = -35

and

Solving for a and b

a+ b = 2

b= 2 - a

a* (2 - a) =-35

2a - a² = -35

a² -2a - 35 =0

a² -7a +5a -35 =0

a( a-7) +5 ( a - 7) =0

(a+5 ) ( a- 7 ) = 0

a = -5 and a= 7

when a = -5 , b = 2+5 = 7

When a = 7, b= -5

So the two numbers are

-5 and 7