What are the solutions to the equation 2x^3+1=x^2+2x ?

The solutions to the equation 2x^3+1=x^2+2x are x= 1/2 ,x=-1,x=1

Find the zeros of 2x^3+1=x^2+2x

The zeros of 2x^3+1=x^2+2x are x= 1/2 ,x=-1,x=1

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2 x^{3} + 1 = x^{2} + 2 x

x = \frac{1}{2}, x = - 1, x = 1

Decimal Notation

x = 0.5, x = - 1, x = 1

Solution steps

2 x^{3} + 1 = x^{2} + 2 x

Move

2 x

to the left side

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

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or x + 1 = 0 or x - 1 = 0

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = \frac{1}{2}, x = - 1, x = 1

x^{633} = 9

z^{4} + 64 = 0

x^{3} - x^{2} - 16 x + 16 = 0

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

2 = (1 + x)^{12}

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