SOLUTION: I need help solving this word problem: The sum of two numbers is 10. Their product is -24. Find the numbers. Write a complete solution

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Question 6763: I need help solving this word problem:
The sum of two numbers is 10. Their product is -24. Find the numbers. Write a complete solution
Answer by Earlsdon(6294) (Show Source):
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Try this!
Let the two numbers be x and y.
Then:
x + y = 10 Rewrite as: x = 10 - y and substitute into equation below.
xy = -24.
(10 - y)Y = -24 Solve for y.
10y - y^2 = -24 Add 24 to both sides and put into standard form.
y^2 - 10y - 24 = 0 Solve the quadratic by factoring.
(y + 2)(y - 12) = 0 Apply the zero product principle.
y + 2 = 0, y = -2
y - 12 = 0, y = 12
Now substitute these values of y into the original equations:
x = 10 - y
x = 10 - (-2)
x = 12
And:
x = 10 -y
x = 10 - 12
x = -2
The two numbers are: -2 and 12
Check:
12 + (-2) = 10, and
12(-2) = -24