SOLUTION: PLEASE HELP ME SOLVE THIS PROBLEM. (x2+5) = x+3 The answer is -2/3 but I don't know how to arrive at this. I worked for several hours on this but had no luck.

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: PLEASE HELP ME SOLVE THIS PROBLEM. (x2+5) = x+3 The answer is -2/3 but I don't know how to arrive at this. I worked for several hours on this but had no luck.      Log On

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Question 25593: PLEASE HELP ME SOLVE THIS PROBLEM. (x2+5) = x+3 The answer is -2/3 but I don't know how to arrive at this. I worked for several hours on this but had no luck.
Found 2 solutions by AnlytcPhil, stanbon:
Answer by AnlytcPhil(1116) About Me  (Show Source):
You can put this solution on YOUR website!
(x²+5) = x+3
The answer is NOT -2/3

Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume your x2 means x^2.
You have x^2+5=x+3
x^2-x+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%2B-1x%2B2+=+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=%28-1%29%5E2-4%2A1%2A2=-7.

The discriminant -7 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 -7 is + or - sqrt%28+7%29+=+2.64575131106459.

The solution is x%5B12%5D+=+%28--1%2B-+i%2Asqrt%28+-7+%29%29%2F2%5C1+=++%28--1%2B-+i%2A2.64575131106459%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B2+%29

Cheers,
Stan H.