What are the solutions to the equation x^3-2x^2=75 ?

The solutions to the equation x^3-2x^2=75 are x=5,x=-3/2+i(sqrt(51))/2 ,x=-3/2-i(sqrt(51))/2

Find the zeros of x^3-2x^2=75

The zeros of x^3-2x^2=75 are x=5,x=-3/2+i(sqrt(51))/2 ,x=-3/2-i(sqrt(51))/2

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x^{3} - 2 x^{2} = 75

x = 5, x = - \frac{3}{2} + i \frac{51}{2}, x = - \frac{3}{2} - i \frac{51}{2}

Solution steps

x^{3} - 2 x^{2} = 75

Move

75

to the left side

x^{3} - 2 x^{2} - 75 = 0

Factor

x^{3} - 2 x^{2} - 75 : (x - 5) (x^{2} + 3 x + 15)

(x - 5) (x^{2} + 3 x + 15) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{2} + 3 x + 15 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{2} + 3 x + 15 = 0 : x = - \frac{3}{2} + i \frac{51}{2}, x = - \frac{3}{2} - i \frac{51}{2}

The solutions are

x = 5, x = - \frac{3}{2} + i \frac{51}{2}, x = - \frac{3}{2} - i \frac{51}{2}

\frac{x}{3} + \frac{3}{9} = x^{4} + 75

- 3 x^{3} - 7 x + 6 = 0

3 x^{3} - 19 x - 5 = 0

x^{4} - 7 x^{2} - 8 = 0

2 x^{3} - 12 x^{2} + 18 = 0

What are the solutions to the equation x^3-2x^2=75 ?
The solutions to the equation x^3-2x^2=75 are x=5,x=-3/2+i(sqrt(51))/2 ,x=-3/2-i(sqrt(51))/2
Find the zeros of x^3-2x^2=75
The zeros of x^3-2x^2=75 are x=5,x=-3/2+i(sqrt(51))/2 ,x=-3/2-i(sqrt(51))/2