SOLUTION: How would you do these problems??? 5. Solve: 6x2 + 12x = 0 6. Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 - 2

Algebra ->  Signed-numbers -> SOLUTION: How would you do these problems??? 5. Solve: 6x2 + 12x = 0 6. Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 - 2      Log On


   

Question 195103: How would you do these problems???

5. Solve: 6x2 + 12x = 0



6. Solve each problem by using the quadratic formula. Write solutions in simplest radical form.
2x2 - 2x -1 = 0
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2+%2B+12x+=+0
6x%28x+%2B+2%29+=+0
So either 6x=0 or x+2 = 0
x =0 or x = -2

2)
2x%5E2+-+2x+-1+=+0+
Use this URL for quadratic equations --> http://www.algebra.com/algebra/homework/quadratic/quadratic.solver
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-2x%2B-1+=+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=%28-2%29%5E2-4%2A2%2A-1=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C2+=+1.36602540378444
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C2+=+-0.366025403784439

Quadratic expression 2x%5E2%2B-2x%2B-1 can be factored:
2x%5E2%2B-2x%2B-1+=+2%28x-1.36602540378444%29%2A%28x--0.366025403784439%29
Again, the answer is: 1.36602540378444, -0.366025403784439. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-2%2Ax%2B-1+%29