What are the solutions to the equation 5x^3+45x=2x^2+18 ?

The solutions to the equation 5x^3+45x=2x^2+18 are x= 2/5 ,x=3i,x=-3i

Find the zeros of 5x^3+45x=2x^2+18

The zeros of 5x^3+45x=2x^2+18 are x= 2/5 ,x=3i,x=-3i

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5 x^{3} + 45 x = 2 x^{2} + 18

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

Solution steps

5 x^{3} + 45 x = 2 x^{2} + 18

Move

18

to the left side

5 x^{3} + 45 x - 18 = 2 x^{2}

Move

2 x^{2}

to the left side

5 x^{3} + 45 x - 18 - 2 x^{2} = 0

Write in the standard form

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

5 x^{3} - 2 x^{2} + 45 x - 18 = 0

Factor

5 x^{3} - 2 x^{2} + 45 x - 18 : (5 x - 2) (x^{2} + 9)

(5 x - 2) (x^{2} + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 x - 2 = 0 or x^{2} + 9 = 0

Solve

5 x - 2 = 0 : x = \frac{2}{5}

Solve

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

The solutions are

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

5 X (X + 6)^{2} = 0

3 x^{4} = 1536 x

16 x^{3} + 64 x^{2} - x - 4 = 0

6 x^{4} - 5 x^{3} - 38 x^{2} - 5 x + 6 = 0

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

What are the solutions to the equation 5x^3+45x=2x^2+18 ?
The solutions to the equation 5x^3+45x=2x^2+18 are x= 2/5 ,x=3i,x=-3i
Find the zeros of 5x^3+45x=2x^2+18
The zeros of 5x^3+45x=2x^2+18 are x= 2/5 ,x=3i,x=-3i