What are the solutions to the equation x^3+5x^2=x+5 ?

The solutions to the equation x^3+5x^2=x+5 are x=-5,x=-1,x=1

Find the zeros of x^3+5x^2=x+5

The zeros of x^3+5x^2=x+5 are x=-5,x=-1,x=1

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x^{3} + 5 x^{2} = x + 5

x = - 5, x = - 1, x = 1

Solution steps

x^{3} + 5 x^{2} = x + 5

Move

5

to the left side

x^{3} + 5 x^{2} - 5 = x

Move

x

to the left side

x^{3} + 5 x^{2} - 5 - x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + 5 x^{2} - x - 5 = 0

Factor

x^{3} + 5 x^{2} - x - 5 : (x + 5) (x + 1) (x - 1)

(x + 5) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 5 = 0 or x + 1 = 0 or x - 1 = 0

Solve

x + 5 = 0 : x = - 5

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = - 5, x = - 1, x = 1

y^{3} + 2 y^{2} + 4 y + 2 = 0

18 x^{5} - 21 x^{4} - 9 x^{3} = 0

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

99 = c^{3}

5 (x + 2) = 2 (x^{5})

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