Answer:
The Two numbers are 7 and -3.
Step-by-step explanation:
For this problem, the first thing we need to do is rewrite what we are given in mathematical terms, or equations that we can use to solve our problem at hand. We can say that:
X = <em>"one number" </em>
and
X+10 = <em>"our other number".</em>
then with our given information and newly defined mathematical terms, we would then combine both of them and formulate it into an equation that we can use to find the two numbers:
= x(x+10) = -21 (Next, we expand this equation to:) --->
= X2+10x-21=0 (Side Note: the "x2" is x squared.).
= X2+10x-21 = 0 (add 21 to the other side to get)
= X2+10x +21 = 0 (this is the equation that we will use to find the two numbers)
Next step is to solve by factoring the equation X2+10x+21=0
An easy way to approach factoring an equation of this format is to think..
"<em>What two numbers can add up to equal ten? (10x) and also multiply to equal 21 (+21) ? "</em>
In our case, our two numbers are 7 and 3. (Because 7 plus 3 equals ten, and also 7 times 3 equals 21.)
So, with that information, : X2+10x+21 factored equals
(x+3)(x+7) = 0.
Next, we set both X+3 and X+7 equal to zero and solve for x to find the two numbers
= ( x+3) = 0 (3-3 = 0 0-3 = -3), so, X= -3
= (x+7) = 0 (7-7 = 0 0-7 = -7), so, X = -7
So with the work above we found the two numbers we need, However, the question specifically stated that the product of the two numbers is negative 21, and we currently have positive 21 (Because neg 7 times neg 3 = positive 21).
So, with this, our last step is to use one of the two numbers that we found (X= -3 or X= -7) in the second equation that we made in the beginning to find the last number that we need.
We know that a negative number times a positive number equals a negative number, so with this fact in mind, we revisit one of our first equations while keeping our original question in mind that:
<em>"one number is </em><em>10</em><em> more than another number "</em>
With that in mind, the only combination that has the highest chance of working in accordance to the question we have is:
X=-3
So based on that observation, we have assumed that -3 is our first number. We need to <em>prove</em> that it is the right number by plugging it into the equation below:
So, if we plug in -3 in our equation that we made in the beginning (X+10 = "our other number"), then we find:
= -3+10 = 7 which is our second and final number!
Therefore, the two numbers are 7 and -3 because 7 is 10 more than -3,
and the product of both numbers are -21.
I hope this helps, Thanks for your time!
