SOLUTION: 3x+x(x-2)=4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 3x+x(x-2)=4      Log On


   

Question 102487: 3x+x(x-2)=4
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2Bx%28x-2%29=4.
First, solve the parenthesis by multiplying x-2 by x = x^2 - 2x.
3x%2Bx%5E2-2x=4
Second, collect terms.
x%5E2%2Bx=4
Third, subtract 4 from both sides.
x%5E2%2Bx-4=0
That is the equation in standard form, which can be solved with the quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-4+=+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=%281%29%5E2-4%2A1%2A-4=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+1.56155281280883
x%5B2%5D+=+%28-%281%29-sqrt%28+17+%29%29%2F2%5C1+=+-2.56155281280883

Quadratic expression 1x%5E2%2B1x%2B-4 can be factored:
1x%5E2%2B1x%2B-4+=+1%28x-1.56155281280883%29%2A%28x--2.56155281280883%29
Again, the answer is: 1.56155281280883, -2.56155281280883. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-4+%29