SOLUTION: Problem: Solve using the quadratic formula: 5x(squared)-2x+9=0 x= 2 times the square root of 2(squared)-4(5)(9) over 5(2). x= 2 times the square root of 4-180 over 10. x= 2 ti

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Problem: Solve using the quadratic formula: 5x(squared)-2x+9=0 x= 2 times the square root of 2(squared)-4(5)(9) over 5(2). x= 2 times the square root of 4-180 over 10. x= 2 ti      Log On


   

Question 475389: Problem: Solve using the quadratic formula: 5x(squared)-2x+9=0
x= 2 times the square root of 2(squared)-4(5)(9) over 5(2).
x= 2 times the square root of 4-180 over 10.
x= 2 times +or- the square root of -176 over 10.
x= +or- the square root of -176 over 5.
That is as far as I've gotten in the problem. I know that the answer is supposed to be 1/5 +- 2(square root of 11)/5i. I'm having a difficult time figuring out how to get there from the last step of the problem I listed.
Thank you.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula:
5x^2-2x+9=0
x= 2 times the square root of 2(squared)-4(5)(9) over 5(2)
-------- It's 2 ± the sqrt .... , not times.
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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 5x%5E2%2B-2x%2B9+=+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%2A5%2A9=-176.

The discriminant -176 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -176 is + or - sqrt%28+176%29+=+13.2664991614216.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B9+%29

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x= 2 times the square root of 4-180 over 10.
x= 2 times +or- the square root of -176 over 10.
x= +or- the square root of -176 over 5.
That is as far as I've gotten in the problem. I know that the answer is supposed to be 1/5 +- 2(square root of 11)/5i. I'm having a difficult time figuring out how to get there from the last step of the problem I listed.