SOLUTION: what is the standard form of x-36=x^2-11x

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Question 246280: what is the standard form of
x-36=x^2-11x
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

standard form is is like ax^2+bx+c=0
x-36=x^2-11x
let's combine and simplify
subtract x from both sides
-36=x^2-12x
add 36 to both sides
0=x^2-12x+36
change sides
x^2-12x+36=0
a=1, b=-12 and c=36
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B36+=+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=%28-12%29%5E2-4%2A1%2A36=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-12%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-12x%2B36+=+1%28x-6%29%2A%28x-6%29

Again, the answer is: 6, 6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B36+%29