What are the solutions to the equation m^2+40*m+1/(16*10^{-4)}=0 ?

The solutions to the equation m^2+40*m+1/(16*10^{-4)}=0 are m=-20+15i,m=-20-15i

Find the zeros of m^2+40*m+1/(16*10^{-4)}=0

The zeros of m^2+40*m+1/(16*10^{-4)}=0 are m=-20+15i,m=-20-15i

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m^{2} + 40 \cdot m + \frac{1}{16 \cdot 1 0 ^{- 4}} = 0

m = - 20 + 15 i, m = - 20 - 15 i

Solution steps

m^{2} + 40 m + \frac{1}{16 \cdot 1 0 ^{- 4}} = 0

Simplify

16 \cdot 1 0^{- 4} : \frac{1}{625}

m^{2} + 40 m + \frac{1}{\frac{1}{625}} = 0

Multiply both sides by

\frac{1}{625}

\frac{m ^{2}}{625} + \frac{8 m}{125} + 1 = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- \frac{8}{125} \pm ( \frac{8}{125} ) ^{2} - 4 \cdot \frac{1}{625} \cdot 1}{2 \cdot \frac{1}{625}}

Simplify

(\frac{8}{125})^{2} - 4 \cdot \frac{1}{625} \cdot 1 : i \frac{6}{125}

m_{1, 2} = \frac{- \frac{8}{125} \pm i \frac{6}{125}}{2 \cdot \frac{1}{625}}

Separate the solutions

m_{1} = \frac{- \frac{8}{125} + i \frac{6}{125}}{2 \cdot \frac{1}{625}}, m_{2} = \frac{- \frac{8}{125} - i \frac{6}{125}}{2 \cdot \frac{1}{625}}

m = \frac{- \frac{8}{125} + i \frac{6}{125}}{2 \frac{1}{625}} : - 20 + 15 i

m = \frac{- \frac{8}{125} - i \frac{6}{125}}{2 \frac{1}{625}} : - 20 - 15 i

The solutions to the quadratic equation are:

m = - 20 + 15 i, m = - 20 - 15 i

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What are the solutions to the equation m^2+40*m+1/(16*10^{-4)}=0 ?
The solutions to the equation m^2+40*m+1/(16*10^{-4)}=0 are m=-20+15i,m=-20-15i
Find the zeros of m^2+40*m+1/(16*10^{-4)}=0
The zeros of m^2+40*m+1/(16*10^{-4)}=0 are m=-20+15i,m=-20-15i