# SOLUTION: Find the two numbers whose sum is 50 and whose product is 621.

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Question 223934: Find the two numbers whose sum is 50 and whose product is 621.

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Find the two numbers whose sum is 50 and whose product is 621.

Step 1. Let x be one number.

Step 2. Let 50-x be the other number since the sum is 50.

Step 3. Then, x(50-x)=621 or or

Step 4. To solve, use quadratic formula given as

where a=1, b=-50, and c=621

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 27, 23. Here's your graph:

(please ignore the graph since it's the numbers are out of scale)

Step 5. ANSWER: The numbers are 23 and 27.

I hope the above steps were helpful.