What are the solutions to the equation x^3+8x^2=x+8 ?

The solutions to the equation x^3+8x^2=x+8 are x=-8,x=-1,x=1

Find the zeros of x^3+8x^2=x+8

The zeros of x^3+8x^2=x+8 are x=-8,x=-1,x=1

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

x = - 8, x = - 1, x = 1

Solution steps

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

Move

8

to the left side

x^{3} + 8 x^{2} - 8 = x

Move

x

to the left side

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

Write in the standard form

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

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

Factor

x^{3} + 8 x^{2} - x - 8 : (x + 8) (x + 1) (x - 1)

(x + 8) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 8 = 0 or x + 1 = 0 or x - 1 = 0

Solve

x + 8 = 0 : x = - 8

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = - 8, x = - 1, x = 1

a^{3} = 27

x^{3} + x = 8

70 \cdot 9 = 7 x^{100} - 1

x^{3} + 4 = 0

x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0

What are the solutions to the equation x^3+8x^2=x+8 ?
The solutions to the equation x^3+8x^2=x+8 are x=-8,x=-1,x=1
Find the zeros of x^3+8x^2=x+8
The zeros of x^3+8x^2=x+8 are x=-8,x=-1,x=1