Question

5 m2 + 2m +1= 0
solve the quadratic equation​

Answer 1

Answer:

$\boxed{\mathfrak{m = - \frac{1}{5} \pm \frac{2i}{5}}}$

Step-by-step explanation:

$\sf Solve \: for \: m: \\ \sf \implies 5 m^2 + 2 m + 1 = 0 \\ \\ \sf Divide \: both \: sides \: by \: 5: \\ \sf \implies m^2 + \frac{2m}{5} + \frac{1}{5} = 0 \\ \\ \sf Subtract \: \frac{1}{5} \: from \: both \: sides: \\ \sf \implies m^2 + \frac{2m}{5} = - \frac{1}{5} \\ \\ \sf Add \: 1/25 \: to \: both \: sides: \\ \sf \implies m^2 + \frac{2m}{5} + \frac{1}{25} = - \frac{1}{5} + \frac{1}{25} \\ \\ \sf \implies {m}^{2} + \frac{2m}{5} + \frac{1}{25} = \frac{ - 5 + 1}{25} \\ \\ \sf \implies {m}^{2} + \frac{2m}{5} + \frac{1}{25} = - \frac{4}{25} \\ \\ \sf Write \: the \: left \: hand \: side \: as \: a \: square: \\ \sf \implies {m}^{2} + \frac{m}{5} + \frac{m}{5} + \frac{1}{25} = - \frac{4}{25} \\ \\ \sf \implies m(m + \frac{1}{5} ) + \frac{1}{5} (m + \frac{1}{5} ) = - \frac{4}{5} \\ \\ \sf \implies {(m + \frac{1}{5} )}^{2} = - \frac{4}{25} \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf \implies \sqrt{ {(m + \frac{1}{5}) }^{2} } = \sqrt{ - \frac{4}{25} } \\ \\ \sf \implies m + \frac{1}{5} = \pm \frac{2i}{5} \\ \\ \sf Subtract \: \frac{1}{5} \: from \: both \: sides: \\ \sf \implies m = - \frac{1}{5} \pm \frac{2i}{5}$

Answer 2

$\huge\underline\bold{AnSwEr,}$

$\sf Solve \: for \: m: \\ \sf \implies 5 m^2 + 2 m + 1 = 0 \\ \\ \sf Divide \: both \: sides \: by \: 5: \\ \sf \implies m^2 + \frac{2m}{5} + \frac{1}{5} = 0 \\ \\ \sf Subtract \: \frac{1}{5} \: from \: both \: sides: \\ \sf \implies m^2 + \frac{2m}{5} = - \frac{1}{5} \\ \\ \sf Add \: 1/25 \: to \: both \: sides: \\ \sf \implies m^2 + \frac{2m}{5} + \frac{1}{25} = - \frac{1}{5} + \frac{1}{25} \\ \\ \sf \implies {m}^{2} + \frac{2m}{5} + \frac{1}{25} = \frac{ - 5 + 1}{25} \\ \\ \sf \implies {m}^{2} + \frac{2m}{5} + \frac{1}{25} = - \frac{4}{25} \\ \\ \sf Write \: the \: left \: hand \: side \: as \: a \: square: \\ \sf \implies {m}^{2} + \frac{m}{5} + \frac{m}{5} + \frac{1}{25} = - \frac{4}{25} \\ \\ \sf \implies m(m + \frac{1}{5} ) + \frac{1}{5} (m + \frac{1}{5} ) = - \frac{4}{5} \\ \\ \sf \implies {(m + \frac{1}{5} )}^{2} = - \frac{4}{25} \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf \implies \sqrt{ {(m + \frac{1}{5}) }^{2} } = \sqrt{ - \frac{4}{25} } \\ \\ \sf \implies m + \frac{1}{5} = \pm \frac{2i}{5} \\ \\ \sf Subtract \: \frac{1}{5} \: from \: both \: sides: \\ \sf \implies m = - \frac{1}{5} \pm \frac{2i}{5}$

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