What are the solutions to the equation 2x^3+9=x^2+18x ?

The solutions to the equation 2x^3+9=x^2+18x are x= 1/2 ,x=-3,x=3

Find the zeros of 2x^3+9=x^2+18x

The zeros of 2x^3+9=x^2+18x are x= 1/2 ,x=-3,x=3

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

x = \frac{1}{2}, x = - 3, x = 3

Decimal Notation

x = 0.5, x = - 3, x = 3

Solution steps

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

Move

18 x

to the left side

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

Move

x^{2}

to the left side

2 x^{3} + 9 - 18 x - x^{2} = 0

Write in the standard form

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

2 x^{3} - x^{2} - 18 x + 9 = 0

Factor

2 x^{3} - x^{2} - 18 x + 9 : (2 x - 1) (x + 3) (x - 3)

(2 x - 1) (x + 3) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or x + 3 = 0 or x - 3 = 0

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = \frac{1}{2}, x = - 3, x = 3

36 x^{3} = 144 x

- 1000 = m^{3}

x^{4} - 13 x^{2} - 48 = 0

x^{3} + 3 x^{2} + 3 x - 1 = 0

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

What are the solutions to the equation 2x^3+9=x^2+18x ?
The solutions to the equation 2x^3+9=x^2+18x are x= 1/2 ,x=-3,x=3
Find the zeros of 2x^3+9=x^2+18x
The zeros of 2x^3+9=x^2+18x are x= 1/2 ,x=-3,x=3