SOLUTION: what number is used to complete the sqaure for the equation x^2=20x a.)-100 b.)-10 c.)10 d.)100

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Question 325626: what number is used to complete the sqaure for the equation x^2=20x
a.)-100
b.)-10
c.)10
d.)100
Found 2 solutions by AAfter Search, JBarnum:
Answer by AAfter Search(61) About Me  (Show Source):
You can put this solution on YOUR website!
x^2=20x
=> x^2 - 20x = 0
To make the quadratic equation a complete square, the determinant should be zero.
Hence, if the required equation is x^2 - 20x +c = 0
Determinant = (-20)^2 - 4 x 1 x c = 0
=> 400 = 4c
=> c = 400/4 = 100.
Answer: d

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
+100


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-20x%2B100+=+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=%28-20%29%5E2-4%2A1%2A100=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-20%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-20x%2B100+=+1%28x-10%29%2A%28x-10%29

Again, the answer is: 10, 10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B100+%29