SOLUTION: using the Quadratic Formula how can i solve ½x^2 + x = 1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: using the Quadratic Formula how can i solve ½x^2 + x = 1       Log On


   

Question 630080: using the Quadratic Formula how can i solve ½x^2 + x = 1
Found 2 solutions by richwmiller, graphmatics:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
multiply by 2 to make it easier to work with.
x^2+2x=2
x^2+2x-2=0
now use the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-2+=+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=%282%29%5E2-4%2A1%2A-2=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-%282%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+0.732050807568877
x%5B2%5D+=+%28-%282%29-sqrt%28+12+%29%29%2F2%5C1+=+-2.73205080756888

Quadratic expression 1x%5E2%2B2x%2B-2 can be factored:
1x%5E2%2B2x%2B-2+=+1%28x-0.732050807568877%29%2A%28x--2.73205080756888%29
Again, the answer is: 0.732050807568877, -2.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-2+%29

Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
+0.5%2Ax%2Ax%2Bx-1=0+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.5x%5E2%2B1x%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=%281%29%5E2-4%2A0.5%2A-1=3.

Discriminant d=3 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+3+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+3+%29%29%2F2%5C0.5+=+0.732050807568877
x%5B2%5D+=+%28-%281%29-sqrt%28+3+%29%29%2F2%5C0.5+=+-2.73205080756888

Quadratic expression 0.5x%5E2%2B1x%2B-1 can be factored:
0.5x%5E2%2B1x%2B-1+=+0.5%28x-0.732050807568877%29%2A%28x--2.73205080756888%29
Again, the answer is: 0.732050807568877, -2.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B1%2Ax%2B-1+%29