What are the solutions to the equation a^3+a^2=80 ?

The solutions to the equation a^3+a^2=80 are a=4,a=-5/2+i(sqrt(55))/2 ,a=-5/2-i(sqrt(55))/2

Find the zeros of a^3+a^2=80

The zeros of a^3+a^2=80 are a=4,a=-5/2+i(sqrt(55))/2 ,a=-5/2-i(sqrt(55))/2

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a^{3} + a^{2} = 80

a = 4, a = - \frac{5}{2} + i \frac{55}{2}, a = - \frac{5}{2} - i \frac{55}{2}

Solution steps

a^{3} + a^{2} = 80

Move

80

to the left side

a^{3} + a^{2} - 80 = 0

Factor

a^{3} + a^{2} - 80 : (a - 4) (a^{2} + 5 a + 20)

(a - 4) (a^{2} + 5 a + 20) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a - 4 = 0 or a^{2} + 5 a + 20 = 0

Solve

a - 4 = 0 : a = 4

Solve

a^{2} + 5 a + 20 = 0 : a = - \frac{5}{2} + i \frac{55}{2}, a = - \frac{5}{2} - i \frac{55}{2}

The solutions are

a = 4, a = - \frac{5}{2} + i \frac{55}{2}, a = - \frac{5}{2} - i \frac{55}{2}

x^{3} - 2 x^{2} - 9 x + 18

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

x^{5} + 8 x^{3} = 0

0.001 x^{3} - 2 x + 30 = 0

4 x^{9} = 12 x^{3}

What are the solutions to the equation a^3+a^2=80 ?
The solutions to the equation a^3+a^2=80 are a=4,a=-5/2+i(sqrt(55))/2 ,a=-5/2-i(sqrt(55))/2
Find the zeros of a^3+a^2=80
The zeros of a^3+a^2=80 are a=4,a=-5/2+i(sqrt(55))/2 ,a=-5/2-i(sqrt(55))/2