Question 159256: How do you solve: n^2 - 10n = -21 ?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How do you solve: n^2 - 10n = -21 ?
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Put it into quadratic form:
n^2 - 10n + 21 = 0
One way is to factor it.
It will factor into (n - a)*(n - b)
a*b is 21
a+b is 10
a and b have the same sign, since their product, a*b, is positive.
The only (integer) factors that work to make a*b 21 are:
21*1 and 7*3.
21 and 1 add up to 22, so that's no good.
7 and 3 total 10, which is the coefficient of the middle term, so that's the ones we're looking for.
(n - 3)*(n - 7) = 0
So n = 3, n = 7
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You can use the quadratic equation, too.
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
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: 7, 3.
Here's your graph:
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The onsite solver always uses x, so sub n for x.
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