Hint: If x is one number, then the other is -17-x

# the sum of two numbers is -17. Their product is 66. Find the numbers

A = one number
B = the other number
A + B = -17 ← Call this eq1
A = - B - 17

A x B = 66 ← call this eq2

A = 66/B  ← eq3

substitute eq3 to eq1

66/B + B = -17

66 + B² = -17B

B² + 17B  + 66 = 0

B = [-b ±√B² - 4ac]/2a

B = [-17 ±√(-17)² - 4(66)] / 2

B = -17 ±√289 - 264 ]/2

B = [ -17 ± √25]/2

B = [ -17 + 5]/2

B = -12 /2

B = - 6

Substitute B = -6 to eq 2

A x B = 66 ← call this eq2

A = 66 / - 6

A = - 11

by Level 3 User (2.7k points)
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