What are the solutions to the equation 98x-49=2x^3-x^2 ?

The solutions to the equation 98x-49=2x^3-x^2 are x= 1/2 ,x=-7,x=7

Find the zeros of 98x-49=2x^3-x^2

The zeros of 98x-49=2x^3-x^2 are x= 1/2 ,x=-7,x=7

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98 x - 49 = 2 x^{3} - x^{2}

x = \frac{1}{2}, x = - 7, x = 7

Decimal Notation

x = 0.5, x = - 7, x = 7

Solution steps

98 x - 49 = 2 x^{3} - x^{2}

Switch sides

2 x^{3} - x^{2} = 98 x - 49

Move

49

to the left side

2 x^{3} - x^{2} + 49 = 98 x

Move

98 x

to the left side

2 x^{3} - x^{2} + 49 - 98 x = 0

Write in the standard form

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

2 x^{3} - x^{2} - 98 x + 49 = 0

Factor

2 x^{3} - x^{2} - 98 x + 49 : (2 x - 1) (x + 7) (x - 7)

(2 x - 1) (x + 7) (x - 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or x + 7 = 0 or x - 7 = 0

Solve

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

Solve

x + 7 = 0 : x = - 7

Solve

x - 7 = 0 : x = 7

The solutions are

x = \frac{1}{2}, x = - 7, x = 7

x^{4} = - 256

36 x^{4} - 83 x^{2} + 35 = 0

x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 = 0

x^{4} + 5 x^{3} + 3 x^{2} - 9 x = 0

(6 x^{3}) x^{5} = 6 x (3 x^{5})

What are the solutions to the equation 98x-49=2x^3-x^2 ?
The solutions to the equation 98x-49=2x^3-x^2 are x= 1/2 ,x=-7,x=7
Find the zeros of 98x-49=2x^3-x^2
The zeros of 98x-49=2x^3-x^2 are x= 1/2 ,x=-7,x=7