What are the solutions to the equation (q)=q^2+50q+1000 ?

The solutions to the equation (q)=q^2+50q+1000 are q=-49/2+i(sqrt(1599))/2 ,q=-49/2-i(sqrt(1599))/2

Find the zeros of (q)=q^2+50q+1000

The zeros of (q)=q^2+50q+1000 are q=-49/2+i(sqrt(1599))/2 ,q=-49/2-i(sqrt(1599))/2

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(q) = q^{2} + 50 q + 1000

q = - \frac{49}{2} + i \frac{1599}{2}, q = - \frac{49}{2} - i \frac{1599}{2}

Solution steps

(q) = q^{2} + 50 q + 1000

Refine

q = q^{2} + 50 q + 1000

Switch sides

q^{2} + 50 q + 1000 = q

Move

q

to the left side

q^{2} + 49 q + 1000 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- 49 \pm 4 9 ^{2} - 4 \cdot 1 \cdot 1000}{2 \cdot 1}

Simplify

4 9^{2} - 4 \cdot 1 \cdot 1000 : 1599 i

q_{1, 2} = \frac{- 49 \pm 1599 i}{2 \cdot 1}

Separate the solutions

q_{1} = \frac{- 49 + 1599 i}{2 \cdot 1}, q_{2} = \frac{- 49 - 1599 i}{2 \cdot 1}

q = \frac{- 49 + 1599 i}{2 \cdot 1} : - \frac{49}{2} + i \frac{1599}{2}

q = \frac{- 49 - 1599 i}{2 \cdot 1} : - \frac{49}{2} - i \frac{1599}{2}

The solutions to the quadratic equation are:

q = - \frac{49}{2} + i \frac{1599}{2}, q = - \frac{49}{2} - i \frac{1599}{2}

p^{2} = 1

3 x^{2} + 5 x + 3 = 5

(2 x + 3)^{2} = 18

2 x^{2} + 12 = 30

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

What are the solutions to the equation (q)=q^2+50q+1000 ?
The solutions to the equation (q)=q^2+50q+1000 are q=-49/2+i(sqrt(1599))/2 ,q=-49/2-i(sqrt(1599))/2
Find the zeros of (q)=q^2+50q+1000
The zeros of (q)=q^2+50q+1000 are q=-49/2+i(sqrt(1599))/2 ,q=-49/2-i(sqrt(1599))/2