SOLUTION: Find the constant term that should be added to make the following expression a perfect-square trinomial. x^2 + 7x Is it 49?

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Question 42506: Find the constant term that should be added to make the following expression a perfect-square trinomial.
x^2 + 7x
Is it 49?
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 7x + k
(x + 3.5)(x + 3.5) is what we want
xx + 3.5x + 3.5x + 12.25
x^2 + 7x + 12.25
k = 12.25
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B12.25+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%287%29%5E2-4%2A1%2A12.25=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%287%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B7x%2B12.25+=+1%28x--3.5%29%2A%28x--3.5%29

Again, the answer is: -3.5, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B12.25+%29