What are the solutions to the equation x^3+3x^2=24x+72 ?

The solutions to the equation x^3+3x^2=24x+72 are x=-3,x=-2sqrt(6),x=2sqrt(6)

Find the zeros of x^3+3x^2=24x+72

The zeros of x^3+3x^2=24x+72 are x=-3,x=-2sqrt(6),x=2sqrt(6)

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x^{3} + 3 x^{2} = 24 x + 72

x = - 3, x = - 26, x = 26

Decimal

x = - 3, x = - 4.89897 \dots, x = 4.89897 \dots

Solution steps

x^{3} + 3 x^{2} = 24 x + 72

Move

72

to the left side

x^{3} + 3 x^{2} - 72 = 24 x

Move

24 x

to the left side

x^{3} + 3 x^{2} - 72 - 24 x = 0

Write in the standard form

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

x^{3} + 3 x^{2} - 24 x - 72 = 0

Factor

x^{3} + 3 x^{2} - 24 x - 72 : (x + 3) (x + 26) (x - 26)

(x + 3) (x + 26) (x - 26) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x + 26 = 0 or x - 26 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x + 26 = 0 : x = - 26

Solve

x - 26 = 0 : x = 26

The solutions are

x = - 3, x = - 26, x = 26

x (x - 4)^{3} = 0

s^{3} + 5 s^{2} + 24 s + 20 = 0

x^{3} - 5 x^{2} - 25 x + 125 = 0

x^{3} = (- 1 - 3 i)

7 \times x - 9 = 4 \times x^{27}

What are the solutions to the equation x^3+3x^2=24x+72 ?
The solutions to the equation x^3+3x^2=24x+72 are x=-3,x=-2sqrt(6),x=2sqrt(6)
Find the zeros of x^3+3x^2=24x+72
The zeros of x^3+3x^2=24x+72 are x=-3,x=-2sqrt(6),x=2sqrt(6)