SOLUTION: . Complete the square. Then write the trinomial square in factored form. x2 +2/3 x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: . Complete the square. Then write the trinomial square in factored form. x2 +2/3 x       Log On


   

Question 246539: . Complete the square. Then write the trinomial square in factored form.
x2 +2/3 x
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x2 +2/3 x =0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0.666666666666667x%2B0+=+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=%280.666666666666667%29%5E2-4%2A1%2A0=0.444444444444445.

Discriminant d=0.444444444444445 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.666666666666667%2B-sqrt%28+0.444444444444445+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.666666666666667%29%2Bsqrt%28+0.444444444444445+%29%29%2F2%5C1+=+0


Quadratic expression 1x%5E2%2B0.666666666666667x%2B0 can be factored:
1x%5E2%2B0.666666666666667x%2B0+=+1%28x-0%29%2A%28x--0.666666666666667%29
Again, the answer is: 0, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0.666666666666667%2Ax%2B0+%29

complete the square by taking 1/2 (2/3) and squaring it.
(1/3)^2=1/9
add 1/9 to both sides
x2 +2/3 x +1/9=1/9
factor
(x+1/3)^2=1/9
get sqrt
|x+1/3|=1/3
ans one
x+1/3=-1/3
x=-2/3
answer two
x+1/3=1/3
x=0