What are the solutions to the equation 624=300x+3x^3 ?

The solutions to the equation 624=300x+3x^3 are x=2,x=-1+sqrt(103)i,x=-1-sqrt(103)i

Find the zeros of 624=300x+3x^3

The zeros of 624=300x+3x^3 are x=2,x=-1+sqrt(103)i,x=-1-sqrt(103)i

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624 = 300 x + 3 x^{3}

x = 2, x = - 1 + 103 i, x = - 1 - 103 i

Solution steps

624 = 300 x + 3 x^{3}

Switch sides

300 x + 3 x^{3} = 624

Move

624

to the left side

300 x + 3 x^{3} - 624 = 0

Write in the standard form

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

3 x^{3} + 300 x - 624 = 0

Factor

3 x^{3} + 300 x - 624 : 3 (x - 2) (x^{2} + 2 x + 104)

3 (x - 2) (x^{2} + 2 x + 104) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 2 x + 104 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 104 = 0 : x = - 1 + 103 i, x = - 1 - 103 i

The solutions are

x = 2, x = - 1 + 103 i, x = - 1 - 103 i

(x - 1)^{3} = 8

x^{3} - 15 x^{2} + 63 x - 49 = 0

x^{3} - 14 x - 8 = 0

x^{4} - 1

5 x^{4} - 9 x^{2} + 4 = 0

What are the solutions to the equation 624=300x+3x^3 ?
The solutions to the equation 624=300x+3x^3 are x=2,x=-1+sqrt(103)i,x=-1-sqrt(103)i
Find the zeros of 624=300x+3x^3
The zeros of 624=300x+3x^3 are x=2,x=-1+sqrt(103)i,x=-1-sqrt(103)i