What are the solutions to the equation -x^2+x^3+5=5x ?

The solutions to the equation -x^2+x^3+5=5x are x=1,x=-sqrt(5),x=sqrt(5)

Find the zeros of -x^2+x^3+5=5x

The zeros of -x^2+x^3+5=5x are x=1,x=-sqrt(5),x=sqrt(5)

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

x = 1, x = - 5, x = 5

Decimal Notation

x = 1, x = - 2.23606 \dots, x = 2.23606 \dots

Solution steps

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

Move

5 x

to the left side

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

Write in the standard form

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

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

Factor

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

(x - 1) (x + 5) (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 5 = 0 or x - 5 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

The solutions are

x = 1, x = - 5, x = 5

- 4 x^{3} + 24 x^{2} - 36 x = 0

4 x^{3} + 5 x^{2} + 12 x + 15 = 0

x^{4} - 8 x^{2} - 16 = 0

v^{3} = 27

x^{3} = 3937.5

What are the solutions to the equation -x^2+x^3+5=5x ?
The solutions to the equation -x^2+x^3+5=5x are x=1,x=-sqrt(5),x=sqrt(5)
Find the zeros of -x^2+x^3+5=5x
The zeros of -x^2+x^3+5=5x are x=1,x=-sqrt(5),x=sqrt(5)