What are the solutions to the equation x^2-3=(x(x^2-9))/4 ?

The solutions to the equation x^2-3=(x(x^2-9))/4 are x=1,x=(3+sqrt(57))/2 ,x=(3-sqrt(57))/2

Find the zeros of x^2-3=(x(x^2-9))/4

The zeros of x^2-3=(x(x^2-9))/4 are x=1,x=(3+sqrt(57))/2 ,x=(3-sqrt(57))/2

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x^{2} - 3 = \frac{x ( x ^{2} - 9 )}{4}

x = 1, x = \frac{3 + 57}{2}, x = \frac{3 - 57}{2}

Solution steps

x^{2} - 3 = \frac{x ( x ^{2} - 9 )}{4}

Multiply both sides by

4

4 x^{2} - 12 = x (x^{2} - 9)

Expand

x (x^{2} - 9) : x^{3} - 9 x

4 x^{2} - 12 = x^{3} - 9 x

Switch sides

x^{3} - 9 x = 4 x^{2} - 12

Move

12

to the left side

x^{3} - 9 x + 12 = 4 x^{2}

Move

4 x^{2}

to the left side

x^{3} - 9 x + 12 - 4 x^{2} = 0

Write in the standard form

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

x^{3} - 4 x^{2} - 9 x + 12 = 0

Factor

x^{3} - 4 x^{2} - 9 x + 12 : (x - 1) (x^{2} - 3 x - 12)

(x - 1) (x^{2} - 3 x - 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 3 x - 12 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 3 x - 12 = 0 : x = \frac{3 + 57}{2}, x = \frac{3 - 57}{2}

The solutions are

x = 1, x = \frac{3 + 57}{2}, x = \frac{3 - 57}{2}

2 b^{8} - 18 b^{6} = 0

(z - 4)^{3} = 0

55.82 x^{3} - 12 x - 384 = 0

700 (x)^{5} = 210

m^{3} + 2 m + 1 = 0

What are the solutions to the equation x^2-3=(x(x^2-9))/4 ?
The solutions to the equation x^2-3=(x(x^2-9))/4 are x=1,x=(3+sqrt(57))/2 ,x=(3-sqrt(57))/2
Find the zeros of x^2-3=(x(x^2-9))/4
The zeros of x^2-3=(x(x^2-9))/4 are x=1,x=(3+sqrt(57))/2 ,x=(3-sqrt(57))/2