What are the solutions to the equation x^4=24x+32 ?

The solutions to the equation x^4=24x+32 are x=1+sqrt(5),x=1-sqrt(5),x=-1+sqrt(7)i,x=-1-sqrt(7)i

Find the zeros of x^4=24x+32

The zeros of x^4=24x+32 are x=1+sqrt(5),x=1-sqrt(5),x=-1+sqrt(7)i,x=-1-sqrt(7)i

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x^{4} = 24 x + 32

x = 1 + 5, x = 1 - 5, x = - 1 + 7 i, x = - 1 - 7 i

Solution steps

x^{4} = 24 x + 32

Move

32

to the left side

x^{4} - 32 = 24 x

Move

24 x

to the left side

x^{4} - 32 - 24 x = 0

Write in the standard form

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

x^{4} - 24 x - 32 = 0

Factor

x^{4} - 24 x - 32 : (x^{2} - 2 x - 4) (x^{2} + 2 x + 8)

(x^{2} - 2 x - 4) (x^{2} + 2 x + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{2} - 2 x - 4 = 0 or x^{2} + 2 x + 8 = 0

Solve

x^{2} - 2 x - 4 = 0 : x = 1 + 5, x = 1 - 5

Solve

x^{2} + 2 x + 8 = 0 : x = - 1 + 7 i, x = - 1 - 7 i

The solutions are

x = 1 + 5, x = 1 - 5, x = - 1 + 7 i, x = - 1 - 7 i

12 (k^{3} - 4 k^{2} + k + 6) = 0

q^{3} - 10 q^{2} - 5808 = 0

1.05 = (1 + \frac{x}{12})^{12}

3 s^{4} - 14 s^{3} + 20 s^{2} + 10 s + 4 = 0

5 x^{3} - 2 (x^{3} + x) = - x

What are the solutions to the equation x^4=24x+32 ?
The solutions to the equation x^4=24x+32 are x=1+sqrt(5),x=1-sqrt(5),x=-1+sqrt(7)i,x=-1-sqrt(7)i
Find the zeros of x^4=24x+32
The zeros of x^4=24x+32 are x=1+sqrt(5),x=1-sqrt(5),x=-1+sqrt(7)i,x=-1-sqrt(7)i