What are the solutions to the equation x^2+x=x^3 ?

The solutions to the equation x^2+x=x^3 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of x^2+x=x^3

The zeros of x^2+x=x^3 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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x^{2} + x = x^{3}

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 0, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

x^{2} + x = x^{3}

Switch sides

x^{3} = x^{2} + x

Move

x

to the left side

x^{3} - x = x^{2}

Move

x^{2}

to the left side

x^{3} - x - x^{2} = 0

Factor

x^{3} - x - x^{2} : x (x^{2} - x - 1)

x (x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - x - 1 = 0

Solve

x^{2} - x - 1 = 0 : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

The solutions are

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

x^{4} - 8 x^{2} + 15 = 0

r^{5} - 5 r = 3

9 x^{4} = 25 x^{2} - 16

x, x^{3} + y^{3} - z^{3} = 4

x^{3} - 2 x - 5 = 0, (x = 2.0813)

What are the solutions to the equation x^2+x=x^3 ?
The solutions to the equation x^2+x=x^3 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of x^2+x=x^3
The zeros of x^2+x=x^3 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2