Middle term splitting of x²-x-1
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Hope this answer helps!
According to the Quadratic Formula, x , the solution for Ax²+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B²-4AC
x = ————————
2A
In our case, A = 1
B = -1
C = -1
Accordingly, B² - 4AC =
1 - (-4) =
5
Applying the quadratic formula :
1 ± √ 5
x = ————
2
√ 5 , rounded to 4 decimal digits, is 2.2361
So now we are looking at:
x = ( 1 ± 2.236 ) / 2
Two real solutions:
x =(1+√5)/2= 1.618
or:
x =(1-√5)/2=-0.618
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