What are the solutions to the equation w^2=3(w-1) ?

The solutions to the equation w^2=3(w-1) are w= 3/2+i(sqrt(3))/2 ,w= 3/2-i(sqrt(3))/2

Find the zeros of w^2=3(w-1)

The zeros of w^2=3(w-1) are w= 3/2+i(sqrt(3))/2 ,w= 3/2-i(sqrt(3))/2

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w^{2} = 3 (w - 1)

w = \frac{3}{2} + i \frac{3}{2}, w = \frac{3}{2} - i \frac{3}{2}

Solution steps

w^{2} = 3 (w - 1)

Expand

3 (w - 1) : 3 w - 3

w^{2} = 3 w - 3

Move

3

to the left side

w^{2} + 3 = 3 w

Move

3 w

to the left side

w^{2} + 3 - 3 w = 0

Write in the standard form

a x^{2} + b x + c = 0

w^{2} - 3 w + 3 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 3 : 3 i

w_{1, 2} = \frac{- ( - 3 ) \pm 3 i}{2 \cdot 1}

Separate the solutions

w_{1} = \frac{- ( - 3 ) + 3 i}{2 \cdot 1}, w_{2} = \frac{- ( - 3 ) - 3 i}{2 \cdot 1}

w = \frac{- ( - 3 ) + 3 i}{2 \cdot 1} : \frac{3}{2} + i \frac{3}{2}

w = \frac{- ( - 3 ) - 3 i}{2 \cdot 1} : \frac{3}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

w = \frac{3}{2} + i \frac{3}{2}, w = \frac{3}{2} - i \frac{3}{2}

\frac{2 7 ^{\frac{4}{3}}}{2 7 ^{\frac{2}{3}}}

16 x^{2} - 9 = 0

4 x^{3} + 24 x^{2} + 32 x

x^{4} + 2 x^{3} - 23 x^{2} - 60 x

36 x^{2} + 7 x = 4 - 30 x + 7 - 6 x^{2}

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