SOLUTION: 6.Please help me solve using the quadratic formula: x2 – 7x – 1 = -7

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 6.Please help me solve using the quadratic formula: x2 – 7x – 1 = -7       Log On


   

Question 109252This question is from textbook
: 6.Please help me solve using the quadratic formula:
x2 – 7x – 1 = -7
 This question is from textbook

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x2 – 7x – 1 = -7
x^2-7x+6=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B6+=+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=%28-7%29%5E2-4%2A1%2A6=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-7%29-sqrt%28+25+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-7x%2B6 can be factored:
1x%5E2%2B-7x%2B6+=+%28x-6%29%2A%28x-1%29
Again, the answer is: 6, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B6+%29