What are the solutions to the equation x^4=5x+6 ?

The solutions to the equation x^4=5x+6 are x=-1,x=2,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

Find the zeros of x^4=5x+6

The zeros of x^4=5x+6 are x=-1,x=2,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2

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x^{4} = 5 x + 6

x = - 1, x = 2, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Solution steps

x^{4} = 5 x + 6

Move

6

to the left side

x^{4} - 6 = 5 x

Move

5 x

to the left side

x^{4} - 6 - 5 x = 0

Write in the standard form

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

x^{4} - 5 x - 6 = 0

Factor

x^{4} - 5 x - 6 : (x + 1) (x - 2) (x^{2} + x + 3)

(x + 1) (x - 2) (x^{2} + x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 2 = 0 or x^{2} + x + 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + x + 3 = 0 : x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

The solutions are

x = - 1, x = 2, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

x^{3} + 8 x^{2} - 36 x = 288

x^{3} - 9 x^{2} + 27 x = 20

4 x^{4} - 14 x^{2} + 12 = 0

x^{3} - 12 x^{2} + 256 = 0

x^{3} + 4 x^{2} - 10

What are the solutions to the equation x^4=5x+6 ?
The solutions to the equation x^4=5x+6 are x=-1,x=2,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2
Find the zeros of x^4=5x+6
The zeros of x^4=5x+6 are x=-1,x=2,x=-1/2+i(sqrt(11))/2 ,x=-1/2-i(sqrt(11))/2