How to isolate a in this equation? I have

Ormezzani6cuu

Ormezzani6cuu

Answered question

2022-04-07

How to isolate a in this equation?
I have the following equation that I would like to isolate the variable a from, but I am a bit stuck. The variable k is known; however, x and a are unknowns.
x2+a(1a)x12(1a)k=0

Answer & Explanation

embemiaEffoset4rs

embemiaEffoset4rs

Beginner2022-04-08Added 14 answers

Multiply the first equation by 1a to get
(1a)x2+ax12k=0.
This is linear in a; collecting like terms yields
(xx2)a+x212k=0,
and hence if x{0,1} then
a=t12kx2xx2=12kx22kx2kx2.

titemomo8gjz

titemomo8gjz

Beginner2022-04-09Added 10 answers

The equation is x2x+x1a12k(1a)=0, therefore
11a(x12k)=xx2

a=12kx12kx(1x)
for k0,x{0,1,12k}. If k=12 and x=1, then every a1 satisfies the equation. In all other cases either the equation does not exist or no a satisfies it.

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