You can put this solution on YOUR website!
Your method is called "completing the square"...
This site explains it quite nicely:
x^2-2x = 13
Take half the 'b' coefficient and square it:[(1/2)(-2)]^2 = [-1]^1 = 1
x^2-2x+1 = 13+1 (since you added 1 to left, do so on the right - for balance)
(x-1)^2 = 14
x-1 = sqrt(14)
x = 1(+-)sqrt(14)
That's 1 "plus or minus" square root of 14.
4x^2-4x = -3
factor the 4 on the left:
4(x^2-x) = -3
(x^2-x) = -3/4
(x^2-x+(1/4)) = -3/4 + 1/4
(x-(1/2))^2 = -2/4
x-(1/2) = sqrt(-2/4)
x = (1/2)(+-)sqrt(-1/2)
Since the term inside the sqrt is negative -- we have no real solutions -- rather, we have two imaginary solutions.
You could see the same thing using the "quadratic equation" below:
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|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 -32 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 -32 is + or - .
The solution is
Here's your graph: