What are the solutions to the equation x^4=45x+76 ?

The solutions to the equation x^4=45x+76 are x=4,x\approx-1.55796…

Find the zeros of x^4=45x+76

The zeros of x^4=45x+76 are x=4,x\approx-1.55796…

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x^{4} = 45 x + 76

x = 4, x \approx - 1.55796 \dots

Solution steps

x^{4} = 45 x + 76

Move

76

to the left side

x^{4} - 76 = 45 x

Move

45 x

to the left side

x^{4} - 76 - 45 x = 0

Write in the standard form

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

x^{4} - 45 x - 76 = 0

Factor

x^{4} - 45 x - 76 : (x - 4) (x^{3} + 4 x^{2} + 16 x + 19)

(x - 4) (x^{3} + 4 x^{2} + 16 x + 19) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{3} + 4 x^{2} + 16 x + 19 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{3} + 4 x^{2} + 16 x + 19 = 0 : x \approx - 1.55796 \dots

The solutions are

x = 4, x \approx - 1.55796 \dots

x + x^{2} + x^{4} = 2000

x^{3} + x + 3 = 0

3 x^{4} - 8 x^{2} - 4 = 0

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

x^{3} - 5 x^{2} + 2 x - 10 = 0

What are the solutions to the equation x^4=45x+76 ?
The solutions to the equation x^4=45x+76 are x=4,x\approx-1.55796…
Find the zeros of x^4=45x+76
The zeros of x^4=45x+76 are x=4,x\approx-1.55796…