What are the solutions to the equation ax^2=4x-x^2 ?

The solutions to the equation ax^2=4x-x^2 are x=0,x= 4/(1+a);\quad a\ne-1

Find the zeros of ax^2=4x-x^2

The zeros of ax^2=4x-x^2 are x=0,x= 4/(1+a);\quad a\ne-1

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a x^{2} = 4 x - x^{2}

x = 0, x = \frac{4}{1 + a}; a \neq = - 1

Solution steps

a x^{2} = 4 x - x^{2}

Switch sides

4 x - x^{2} = a x^{2}

Move

a x^{2}

to the left side

4 x - x^{2} - a x^{2} = 0

Factor

4 x - x^{2} - a x^{2} : x (- x - a x + 4)

x (- x - a x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or - x - a x + 4 = 0

Solve

- x - a x + 4 = 0 : x = \frac{4}{1 + a}; a \neq = - 1

The solutions to the quadratic equation are:

x = 0, x = \frac{4}{1 + a}; a \neq = - 1

x^{2} - n^{2} x + 2 n = 0

4 x^{2} - 2 x + 5 = 0

(x - 2)^{2} + (x + 4)^{2} = 1

2 x^{2} + 8 x = 10

3 x^{2} - 15 = - 378

What are the solutions to the equation ax^2=4x-x^2 ?
The solutions to the equation ax^2=4x-x^2 are x=0,x= 4/(1+a);\quad a\ne-1
Find the zeros of ax^2=4x-x^2
The zeros of ax^2=4x-x^2 are x=0,x= 4/(1+a);\quad a\ne-1