What are the solutions to the equation x^4=24x+9 ?

The solutions to the equation x^4=24x+9 are x=3,x\approx-0.37418…

Find the zeros of x^4=24x+9

The zeros of x^4=24x+9 are x=3,x\approx-0.37418…

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x^{4} = 24 x + 9

x = 3, x \approx - 0.37418 \dots

Solution steps

x^{4} = 24 x + 9

Move

9

to the left side

x^{4} - 9 = 24 x

Move

24 x

to the left side

x^{4} - 9 - 24 x = 0

Write in the standard form

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

x^{4} - 24 x - 9 = 0

Factor

x^{4} - 24 x - 9 : (x - 3) (x^{3} + 3 x^{2} + 9 x + 3)

(x - 3) (x^{3} + 3 x^{2} + 9 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{3} + 3 x^{2} + 9 x + 3 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{3} + 3 x^{2} + 9 x + 3 = 0 : x \approx - 0.37418 \dots

The solutions are

x = 3, x \approx - 0.37418 \dots

s^{3} + 2 s^{2} + 1 = 0

x^{6} - 7 x^{3} - 8 = 0

6 m^{4} - 15 m^{2} = 9

(x^{2} + 1) (x - 1) = 0

x^{4} + 8 x^{3} + 3 x - 12 = 0

What are the solutions to the equation x^4=24x+9 ?
The solutions to the equation x^4=24x+9 are x=3,x\approx-0.37418…
Find the zeros of x^4=24x+9
The zeros of x^4=24x+9 are x=3,x\approx-0.37418…