What are the solutions to the equation w^2=7(w-6) ?

The solutions to the equation w^2=7(w-6) are w= 7/2+i(sqrt(119))/2 ,w= 7/2-i(sqrt(119))/2

Find the zeros of w^2=7(w-6)

The zeros of w^2=7(w-6) are w= 7/2+i(sqrt(119))/2 ,w= 7/2-i(sqrt(119))/2

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w^{2} = 7 (w - 6)

w = \frac{7}{2} + i \frac{119}{2}, w = \frac{7}{2} - i \frac{119}{2}

Solution steps

w^{2} = 7 (w - 6)

Expand

7 (w - 6) : 7 w - 42

w^{2} = 7 w - 42

Move

42

to the left side

w^{2} + 42 = 7 w

Move

7 w

to the left side

w^{2} + 42 - 7 w = 0

Write in the standard form

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

w^{2} - 7 w + 42 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 1 \cdot 42}{2 \cdot 1}

Simplify

(- 7)^{2} - 4 \cdot 1 \cdot 42 : 119 i

w_{1, 2} = \frac{- ( - 7 ) \pm 119 i}{2 \cdot 1}

Separate the solutions

w_{1} = \frac{- ( - 7 ) + 119 i}{2 \cdot 1}, w_{2} = \frac{- ( - 7 ) - 119 i}{2 \cdot 1}

w = \frac{- ( - 7 ) + 119 i}{2 \cdot 1} : \frac{7}{2} + i \frac{119}{2}

w = \frac{- ( - 7 ) - 119 i}{2 \cdot 1} : \frac{7}{2} - i \frac{119}{2}

The solutions to the quadratic equation are:

w = \frac{7}{2} + i \frac{119}{2}, w = \frac{7}{2} - i \frac{119}{2}

- 3 t + 9 \geq - 21

7 x^{2} y - 27 x y^{2} + 18 y^{3}

r^{2} - 2 r + 2 = 0

(3 u - 5) (8 + u) = 0

4 x^{4} - 13 x^{2} + 9

What are the solutions to the equation w^2=7(w-6) ?
The solutions to the equation w^2=7(w-6) are w= 7/2+i(sqrt(119))/2 ,w= 7/2-i(sqrt(119))/2
Find the zeros of w^2=7(w-6)
The zeros of w^2=7(w-6) are w= 7/2+i(sqrt(119))/2 ,w= 7/2-i(sqrt(119))/2