To find two numbers that multiply to 78 and add up to 29, we can use factoring and algebraic methods. Let's solve this problem together.
Let's assume the two numbers are x and y. We know that:
xy = 78 (since the numbers multiply to 78)
x + y = 29 (since the numbers add up to 29)
We can use these equations to solve for x and y. One way to do this is by substitution. We can rearrange the second equation to express one variable in terms of the other. Let's solve for x:
x = 29 - y
Now we can substitute this expression for x in the first equation:
(29 - y)y = 78
Expanding and rearranging the equation, we get:
y^2 - 29y + 78 = 0
Now we can solve this quadratic equation for y. Factoring or using the quadratic formula will help us find the values of y. After finding the values of y, we can substitute them back into the equation x = 29 - y to find the corresponding values of x.
Let me calculate that for you.