SOLUTION: how would you solve for 7d squared +50d +7

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Question 309113: how would you solve for 7d squared +50d +7
Found 2 solutions by Stitch, profemmanuel2q:
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 7D%5E2+%2B+50D+%2B+7
Set the equation equal to 0.
Then use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aD%5E2%2BbD%2Bc=0 (in our case 7D%5E2%2B50D%2B7+=+0) has the following solutons:

D%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=%2850%29%5E2-4%2A7%2A7=2304.

Discriminant d=2304 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-50%2B-sqrt%28+2304+%29%29%2F2%5Ca.

D%5B1%5D+=+%28-%2850%29%2Bsqrt%28+2304+%29%29%2F2%5C7+=+-0.142857142857143
D%5B2%5D+=+%28-%2850%29-sqrt%28+2304+%29%29%2F2%5C7+=+-7

Quadratic expression 7D%5E2%2B50D%2B7 can be factored:
7D%5E2%2B50D%2B7+=+7%28D--0.142857142857143%29%2A%28D--7%29
Again, the answer is: -0.142857142857143, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B50%2Ax%2B7+%29

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The other way is to unfoil the equation
7D%5E2+%2B+50D+%2B+7+=+0
Find the factors of 7: 1,7
Use the factors of 7 & 1 with the coefficient of the D^2 to get 50
7*7 + 1 = 50
Rewrite the equation
%287D+%2B+1%29%2A%28D+%2B+7%29
Set each factor to 0 and solve for D
7D+%2B+1+=+0
7D+=+-1
highlight%28D+=+-1%2F7%29
--------------------------
D+%2B+7+=+0
highlight_green%28D+=+-7%29

Answer by profemmanuel2q(4) About Me  (Show Source):
You can put this solution on YOUR website!
7d squared +50d +7
7d^2 + 49d + d + 7
7d(d + 7) + 1(d + 7)
(7d + 1)(d + 7)