What are the solutions to the equation w^2-7w+19=0 ?

The solutions to the equation w^2-7w+19=0 are w= 7/2+i(3sqrt(3))/2 ,w= 7/2-i(3sqrt(3))/2

Find the zeros of w^2-7w+19=0

The zeros of w^2-7w+19=0 are w= 7/2+i(3sqrt(3))/2 ,w= 7/2-i(3sqrt(3))/2

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w^{2} - 7 w + 19 = 0

w = \frac{7}{2} + i \frac{3 3}{2}, w = \frac{7}{2} - i \frac{3 3}{2}

Solution steps

w^{2} - 7 w + 19 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 1 \cdot 19}{2 \cdot 1}

Simplify

(- 7)^{2} - 4 \cdot 1 \cdot 19 : 33 i

w_{1, 2} = \frac{- ( - 7 ) \pm 3 3 i}{2 \cdot 1}

Separate the solutions

w_{1} = \frac{- ( - 7 ) + 3 3 i}{2 \cdot 1}, w_{2} = \frac{- ( - 7 ) - 3 3 i}{2 \cdot 1}

w = \frac{- ( - 7 ) + 3 3 i}{2 \cdot 1} : \frac{7}{2} + i \frac{3 3}{2}

w = \frac{- ( - 7 ) - 3 3 i}{2 \cdot 1} : \frac{7}{2} - i \frac{3 3}{2}

The solutions to the quadratic equation are:

w = \frac{7}{2} + i \frac{3 3}{2}, w = \frac{7}{2} - i \frac{3 3}{2}

- 2 w^{2} - 12 w - 9 = 0

4 n^{2} - 22 = 27

20 r^{2} + 37 r + 15

16 y^{2} + 8 y - 15

(m - 3) (m - 4) = 20

What are the solutions to the equation w^2-7w+19=0 ?
The solutions to the equation w^2-7w+19=0 are w= 7/2+i(3sqrt(3))/2 ,w= 7/2-i(3sqrt(3))/2
Find the zeros of w^2-7w+19=0
The zeros of w^2-7w+19=0 are w= 7/2+i(3sqrt(3))/2 ,w= 7/2-i(3sqrt(3))/2