What are the solutions to the equation a^3+a^2=64a+64 ?

The solutions to the equation a^3+a^2=64a+64 are a=-1,a=-8,a=8

Find the zeros of a^3+a^2=64a+64

The zeros of a^3+a^2=64a+64 are a=-1,a=-8,a=8

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a^{3} + a^{2} = 64 a + 64

a = - 1, a = - 8, a = 8

Solution steps

a^{3} + a^{2} = 64 a + 64

Move

64

to the left side

a^{3} + a^{2} - 64 = 64 a

Move

64 a

to the left side

a^{3} + a^{2} - 64 - 64 a = 0

Write in the standard form

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

a^{3} + a^{2} - 64 a - 64 = 0

Factor

a^{3} + a^{2} - 64 a - 64 : (a + 1) (a + 8) (a - 8)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a + 1 = 0 or a + 8 = 0 or a - 8 = 0

Solve

a + 1 = 0 : a = - 1

Solve

a + 8 = 0 : a = - 8

Solve

a - 8 = 0 : a = 8

The solutions are

a = - 1, a = - 8, a = 8

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

y^{4} - 5 y^{2} - 36 = 0

(30 - 4 x) (20 - 2 x) (x) = 0

x^{3} - 30 x^{2} - 1900 x - 18000 = 0

x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 4 = 0

What are the solutions to the equation a^3+a^2=64a+64 ?
The solutions to the equation a^3+a^2=64a+64 are a=-1,a=-8,a=8
Find the zeros of a^3+a^2=64a+64
The zeros of a^3+a^2=64a+64 are a=-1,a=-8,a=8