Question

What multiplies to 200 and adds to 45

Answer 1

Here we answer the question: "What two numbers multiply to 200 and add up to 45?"

The answer to your question is: 5 and 40

Below we illustrate and prove that 5 and 40 multiply to 200 and add up to 45:

5 × 40 = 200
5 + 40 = 45

Are you asking because you are trying to figure out how to factor the following quadratic equation?

x2 + 45x + 200 = 0

If so, the solution to factor the quadratic equation above is:

(x + 5 ) (x + 40)

To summarize, since 5 and 40 multiply to 200 and add up 45, you know that the following is true:

x2 + 45x + 200 = (x + 5 ) (x + 40)

5 and 40

Answer 2

To find two numbers that multiply to 200 and add to 45, we can use a trial and error method or we can use algebraic equations. Here's how to do it using the algebraic method:

Let x and y be the two numbers we're looking for. Then we have:

xy = 200 (equation 1)

x + y = 45 (equation 2)

We can solve for one of the variables in terms of the other in equation 2:

y = 45 - x

Substitute this expression for y into equation 1:

x(45 - x) = 200

Simplify and solve for x:

45x - x^2 = 200

x^2 - 45x + 200 = 0

This is a quadratic equation that we can solve using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -45, and c = 200. Substituting these values, we get:

x = (45 ± sqrt(45^2 - 4(1)(200))) / 2(1)

x = (45 ± sqrt(2025 - 800)) / 2

x = (45 ± sqrt(1225)) / 2

x = (45 ± 35) / 2

We get two possible values of x:

x = 10 or x = 35

Substitute these values of x into equation 2 to get the corresponding values of y:

y = 45 - x

If x = 10, then y = 45 - 10 = 35

If x = 35, then y = 45 - 35 = 10

Therefore, the two numbers that multiply to 200 and add to 45 are 10 and 35.

Explanation: