What are the solutions to the equation w^2=9(w-6) ?

The solutions to the equation w^2=9(w-6) are w= 9/2+i(3sqrt(15))/2 ,w= 9/2-i(3sqrt(15))/2

Find the zeros of w^2=9(w-6)

The zeros of w^2=9(w-6) are w= 9/2+i(3sqrt(15))/2 ,w= 9/2-i(3sqrt(15))/2

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w^{2} = 9 (w - 6)

w = \frac{9}{2} + i \frac{3 15}{2}, w = \frac{9}{2} - i \frac{3 15}{2}

Solution steps

w^{2} = 9 (w - 6)

Expand

9 (w - 6) : 9 w - 54

w^{2} = 9 w - 54

Move

54

to the left side

w^{2} + 54 = 9 w

Move

9 w

to the left side

w^{2} + 54 - 9 w = 0

Write in the standard form

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

w^{2} - 9 w + 54 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 1 \cdot 54}{2 \cdot 1}

Simplify

(- 9)^{2} - 4 \cdot 1 \cdot 54 : 315 i

w_{1, 2} = \frac{- ( - 9 ) \pm 3 15 i}{2 \cdot 1}

Separate the solutions

w_{1} = \frac{- ( - 9 ) + 3 15 i}{2 \cdot 1}, w_{2} = \frac{- ( - 9 ) - 3 15 i}{2 \cdot 1}

w = \frac{- ( - 9 ) + 3 15 i}{2 \cdot 1} : \frac{9}{2} + i \frac{3 15}{2}

w = \frac{- ( - 9 ) - 3 15 i}{2 \cdot 1} : \frac{9}{2} - i \frac{3 15}{2}

The solutions to the quadratic equation are:

w = \frac{9}{2} + i \frac{3 15}{2}, w = \frac{9}{2} - i \frac{3 15}{2}

\frac{x}{7} - 1 = \frac{x}{9} + 5

\frac{2 π}{0.1}

\frac{m - 3 n}{6 m ^{3} n} - \frac{m + 3 n}{6 m ^{3} n}

56 \cdot 618

4 x^{2} + 1 = 12 x

What are the solutions to the equation w^2=9(w-6) ?
The solutions to the equation w^2=9(w-6) are w= 9/2+i(3sqrt(15))/2 ,w= 9/2-i(3sqrt(15))/2
Find the zeros of w^2=9(w-6)
The zeros of w^2=9(w-6) are w= 9/2+i(3sqrt(15))/2 ,w= 9/2-i(3sqrt(15))/2