What are the solutions to the equation 13x=x^3 ?

The solutions to the equation 13x=x^3 are x=0,x=-sqrt(13),x=sqrt(13)

Find the zeros of 13x=x^3

The zeros of 13x=x^3 are x=0,x=-sqrt(13),x=sqrt(13)

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13 x = x^{3}

x = 0, x = - 13, x = 13

Decimal Notation

x = 0, x = - 3.60555 \dots, x = 3.60555 \dots

Solution steps

13 x = x^{3}

Switch sides

x^{3} = 13 x

Move

13 x

to the left side

x^{3} - 13 x = 0

Factor

x^{3} - 13 x : x (x + 13) (x - 13)

x (x + 13) (x - 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 13 = 0 or x - 13 = 0

Solve

x + 13 = 0 : x = - 13

Solve

x - 13 = 0 : x = 13

The solutions are

x = 0, x = - 13, x = 13

x^{4} - 32 x^{2} + 175 = 0

0 = 6 - 6 x^{5}

x^{3} (3 x + 5) = 7 (x + 4)

x, x^{2} (5 - 2 x) = 4

x^{5} = (2 - x)^{3}

What are the solutions to the equation 13x=x^3 ?
The solutions to the equation 13x=x^3 are x=0,x=-sqrt(13),x=sqrt(13)
Find the zeros of 13x=x^3
The zeros of 13x=x^3 are x=0,x=-sqrt(13),x=sqrt(13)