What are the solutions to the equation 5x^3+35x=6x^2+42 ?

The solutions to the equation 5x^3+35x=6x^2+42 are x= 6/5 ,x=sqrt(7)i,x=-sqrt(7)i

Find the zeros of 5x^3+35x=6x^2+42

The zeros of 5x^3+35x=6x^2+42 are x= 6/5 ,x=sqrt(7)i,x=-sqrt(7)i

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5 x^{3} + 35 x = 6 x^{2} + 42

x = \frac{6}{5}, x = 7 i, x = - 7 i

Solution steps

5 x^{3} + 35 x = 6 x^{2} + 42

Move

42

to the left side

5 x^{3} + 35 x - 42 = 6 x^{2}

Move

6 x^{2}

to the left side

5 x^{3} + 35 x - 42 - 6 x^{2} = 0

Write in the standard form

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

5 x^{3} - 6 x^{2} + 35 x - 42 = 0

Factor

5 x^{3} - 6 x^{2} + 35 x - 42 : (5 x - 6) (x^{2} + 7)

(5 x - 6) (x^{2} + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 x - 6 = 0 or x^{2} + 7 = 0

Solve

5 x - 6 = 0 : x = \frac{6}{5}

Solve

x^{2} + 7 = 0 : x = 7 i, x = - 7 i

The solutions are

x = \frac{6}{5}, x = 7 i, x = - 7 i

x^{3} + 7 x^{2} + 24 x + 18 = 0

x^{5} = 4 x^{3}

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

x - 2 x^{2} = 1 + x^{5}

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

What are the solutions to the equation 5x^3+35x=6x^2+42 ?
The solutions to the equation 5x^3+35x=6x^2+42 are x= 6/5 ,x=sqrt(7)i,x=-sqrt(7)i
Find the zeros of 5x^3+35x=6x^2+42
The zeros of 5x^3+35x=6x^2+42 are x= 6/5 ,x=sqrt(7)i,x=-sqrt(7)i