What are the solutions to the equation 50x-25=2x^3-x^2 ?

The solutions to the equation 50x-25=2x^3-x^2 are x= 1/2 ,x=-5,x=5

Find the zeros of 50x-25=2x^3-x^2

The zeros of 50x-25=2x^3-x^2 are x= 1/2 ,x=-5,x=5

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50 x - 25 = 2 x^{3} - x^{2}

x = \frac{1}{2}, x = - 5, x = 5

Decimal Notation

x = 0.5, x = - 5, x = 5

Solution steps

50 x - 25 = 2 x^{3} - x^{2}

Switch sides

2 x^{3} - x^{2} = 50 x - 25

Move

25

to the left side

2 x^{3} - x^{2} + 25 = 50 x

Move

50 x

to the left side

2 x^{3} - x^{2} + 25 - 50 x = 0

Write in the standard form

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

2 x^{3} - x^{2} - 50 x + 25 = 0

Factor

2 x^{3} - x^{2} - 50 x + 25 : (2 x - 1) (x + 5) (x - 5)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

The solutions are

x = \frac{1}{2}, x = - 5, x = 5

x^{3} + 729 = 0

2 x^{3} + 3 x^{2} - 10 x - 15 = 0

z^{5} + 32 i = 0

(x + 2 b) (3 x^{2} - 16 x + 5) = 0

z^{3} + 4 = 5 + i

What are the solutions to the equation 50x-25=2x^3-x^2 ?
The solutions to the equation 50x-25=2x^3-x^2 are x= 1/2 ,x=-5,x=5
Find the zeros of 50x-25=2x^3-x^2
The zeros of 50x-25=2x^3-x^2 are x= 1/2 ,x=-5,x=5