When two numbers multiplied gives -30 when added gives 1
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When two numbers multiplied gives -30 when added gives 1
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Let's call the two numbers "x" and "y." We are given two pieces of information:
1. The product of the numbers is -30:
x * y = -30
2. The sum of the numbers is 1:
x + y = 1
Now, we can use these two equations to solve for the values of x and y. Let's use the second equation to express one of the variables in terms of the other:
x = 1 - y
Now, substitute this expression for x into the first equation:
(1 - y) * y = -30
Simplify and solve for y:
y - y^2 = -30
Now, rearrange the equation:
y^2 - y - 30 = 0
This is a quadratic equation. We can factor it:
(y - 6)(y + 5) = 0
Now, set each factor equal to zero and solve for y:
1. y - 6 = 0
y = 6
2. y + 5 = 0
y = -5
So, there are two possible pairs of numbers:
1. If y = 6, then x = 1 - 6 = -5
2. If y = -5, then x = 1 - (-5) = 6
Therefore, the two pairs of numbers that satisfy the given conditions are (-5, 6) and (6, -5).