Question

write two numbers that multiply to the value on top and add to the value on bottom. -90 × 27

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( xy=-90 \) and \( x + y=27 \).

Step2: Express one variable

From \( x + y=27 \), we can express \( y = 27 - x \).

Step3: Substitute into product equation

Substitute \( y = 27 - x \) into \( xy=-90 \):
\( x(27 - x)=-90 \)
\( 27x-x^{2}=-90 \)
\( x^{2}-27x - 90 = 0 \)

Step4: Solve quadratic equation

We can also try to find two numbers by factoring. We need two numbers that multiply to - 90 and add to 27. Let's list the factor pairs of - 90:

• 90 and - 1 (sum: 89)
• 45 and - 2 (sum: 43)
• 30 and - 3 (sum: 27)

So the two numbers are 30 and - 3.

Answer:

30 and - 3