What are the solutions to the equation solvefor x,f(x^2)=x-x^2 ?

The solutions to the equation solvefor x,f(x^2)=x-x^2 are x=0,x= 1/(1+f);\quad f\ne-1

Find the zeros of solvefor x,f(x^2)=x-x^2

The zeros of solvefor x,f(x^2)=x-x^2 are x=0,x= 1/(1+f);\quad f\ne-1

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solve for

x, f (x^{2}) = x - x^{2}

x = 0, x = \frac{1}{1 + f}; f \neq = - 1

Solution steps

f (x^{2}) = x - x^{2}

Refine

x^{2} f = x - x^{2}

Switch sides

x - x^{2} = x^{2} f

Move

x^{2} f

to the left side

x - x^{2} - x^{2} f = 0

Factor

x - x^{2} - x^{2} f : x (- x - f x + 1)

x (- x - f x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or - x - f x + 1 = 0

Solve

- x - f x + 1 = 0 : x = \frac{1}{1 + f}; f \neq = - 1

The solutions to the quadratic equation are:

x = 0, x = \frac{1}{1 + f}; f \neq = - 1

- (x + 11)^{2} = - 81

2 = 4 x - 6 (x + 1) 4 x - 6 (x + 1)

e x^{2} - x - 2 = 1

3 x^{2} + 9 x + 8 = 0

x^{2} + 19 = - 12 x

What are the solutions to the equation solvefor x,f(x^2)=x-x^2 ?
The solutions to the equation solvefor x,f(x^2)=x-x^2 are x=0,x= 1/(1+f);\quad f\ne-1
Find the zeros of solvefor x,f(x^2)=x-x^2
The zeros of solvefor x,f(x^2)=x-x^2 are x=0,x= 1/(1+f);\quad f\ne-1