What are the solutions to the equation 4x^3+x=x^2 ?

The solutions to the equation 4x^3+x=x^2 are x=0,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8

Find the zeros of 4x^3+x=x^2

The zeros of 4x^3+x=x^2 are x=0,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8

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

x = 0, x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

Solution steps

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

Move

x^{2}

to the left side

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

Factor

4 x^{3} + x - x^{2} : x (4 x^{2} - x + 1)

x (4 x^{2} - x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} - x + 1 = 0

Solve

4 x^{2} - x + 1 = 0 : x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

The solutions are

x = 0, x = \frac{1}{8} + i \frac{15}{8}, x = \frac{1}{8} - i \frac{15}{8}

x^{8} = 729

4 x + 2 x^{2} + 8 x^{3} = 10

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

y^{4} - 10 y^{3} + 5 y^{2} + 100 y + 100 = 0

x^{4} = 45 x + 76

What are the solutions to the equation 4x^3+x=x^2 ?
The solutions to the equation 4x^3+x=x^2 are x=0,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8
Find the zeros of 4x^3+x=x^2
The zeros of 4x^3+x=x^2 are x=0,x= 1/8+i(sqrt(15))/8 ,x= 1/8-i(sqrt(15))/8