SOLUTION: Hello, Original problem: solve using quadratic formula: {{{2x^2+4x+1=0}}}. Using quadratic formula, I arrive at answer: {{{x=-1+or-(2sqrt(2))/4}}}. Using factoring I get:

Algebra ->  Radicals -> SOLUTION: Hello, Original problem: solve using quadratic formula: {{{2x^2+4x+1=0}}}. Using quadratic formula, I arrive at answer: {{{x=-1+or-(2sqrt(2))/4}}}. Using factoring I get:       Log On


   

Question 858732: Hello,
Original problem: solve using quadratic formula: 2x%5E2%2B4x%2B1=0.
Using quadratic formula, I arrive at answer: x=-1%2Bor-%282sqrt%282%29%29%2F4.
Using factoring I get: x=-1%2Bor-%28sqrt%282%29%29%2F2.
My book says answer: x=%28-2%2Bor-sqrt%282%29%29%2F2?
Symplifying fractions containing radicals still really confuses me, so not sure if that is reason for differing answers, or, it is arithmetic errs I haven't spotted.
Thank you,
Allan
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Original problem: solve using quadratic formula: 2x%5E2%2B4x%2B1=0.
Using quadratic formula, I arrive at answer: x=-1%2Bor-%282sqrt%282%29%29%2F4.
Using factoring I get: x=-1%2Bor-%28sqrt%282%29%29%2F2.
My book says answer: x=%28-2%2Bor-sqrt%282%29%29%2F2?
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B1+=+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=%284%29%5E2-4%2A2%2A1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+8+%29%29%2F2%5C2+=+-0.292893218813452
x%5B2%5D+=+%28-%284%29-sqrt%28+8+%29%29%2F2%5C2+=+-1.70710678118655

Quadratic expression 2x%5E2%2B4x%2B1 can be factored:
2x%5E2%2B4x%2B1+=+%28x--0.292893218813452%29%2A%28x--1.70710678118655%29
Again, the answer is: -0.292893218813452, -1.70710678118655. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B1+%29

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All the answers are the same, just different forms.