Question

What multiples to -20 but adds to 19?

Answer 1

• The numbers are - 1 and 20

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Let the numbers be x and y.

Then we have

• xy = - 20,
• x + y = 19.

Solve by substitution

• x = 19 - y

• xy = - 20
• y(19 - y) = -20
• 19y - y² = - 20
• y² - 19y - 20 = 0
• y² - 20y + y - 20 = 0
• y(y - 20) + (y - 20) = 0
• (y + 1) (y - 20) = 0
• y + 1 = 0 and y - 20 = 0
• y = - 1 and y = 20

Find x

• x = 19 - (- 1) = 20 and x = 19 - 20 = - 1