SOLUTION: 14.) Solve each equation by using the quadratic formula -8q^2-2q+1=0

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Question 164915This question is from textbook Elementary and Intermediate
: 14.) Solve each equation by using the quadratic formula
-8q^2-2q+1=0
This question is from textbook Elementary and Intermediate

Found 2 solutions by nerdybill, KnightOwlTutor:
Answer by nerdybill(5404) About Me  (Show Source):
You can put this solution on YOUR website!
-8q^2-2q+1=0
.
Solution: q = {-0.5, 0.25}
.
Details follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aq%5E2%2Bbq%2Bc=0 (in our case -8q%5E2%2B-2q%2B1+=+0) has the following solutons:

q%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%2A-8%2A1=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+36+%29%29%2F2%5Ca.

q%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+36+%29%29%2F2%5C-8+=+-0.5
q%5B2%5D+=+%28-%28-2%29-sqrt%28+36+%29%29%2F2%5C-8+=+0.25

Quadratic expression -8q%5E2%2B-2q%2B1 can be factored:
-8q%5E2%2B-2q%2B1+=+-8%28q--0.5%29%2A%28q-0.25%29
Again, the answer is: -0.5, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B-2%2Ax%2B1+%29

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aq%5E2%2Bbq%2Bc=0 (in our case -8q%5E2%2B-2q%2B1+=+0) has the following solutons:

q%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%2A-8%2A1=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+36+%29%29%2F2%5Ca.

q%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+36+%29%29%2F2%5C-8+=+-0.5
q%5B2%5D+=+%28-%28-2%29-sqrt%28+36+%29%29%2F2%5C-8+=+0.25

Quadratic expression -8q%5E2%2B-2q%2B1 can be factored:
-8q%5E2%2B-2q%2B1+=+-8%28q--0.5%29%2A%28q-0.25%29
Again, the answer is: -0.5, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B-2%2Ax%2B1+%29