SOLUTION: solve he equation {{{(2x-1)^2=x^2-2}}}

Algebra.Com
Question 156376: solve he equation
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!



Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -20 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 -20 is + or - .

The solution is , or
Here's your graph:

The onsite solver doesn't make it clear.
It's (2 +/- sqrt(5)i)/3 where i = sqrt(-1)



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


FOIL the left side


Subtract from both sides. Add to both sides.


Combine like terms.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


or Break up the expression.


or Reduce


So the answers are or


which approximate to or


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