Question

Solve the following qadratic equation by completing square method m²+m upon 2 -3 upon 2=0

Answer 1

Answer:

$m = 1 \: or \: - \frac{ 3}{2}$

Step-by-step explanation:

${m}^{2} + \frac{m}{2} - \frac{3}{2} = 0$

$( {m}^{2} + 2.m. \frac{1}{4} + {( \frac{1}{4} )}^{2} ) - {( \frac{1}{4} )}^{2} - \frac{3}{2} = 0$

${(m + \frac{1}{4} )}^{2} = \frac{1}{16} + \frac{3}{2}$

${(m + \frac{1}{4} )}^{2} = \frac{25}{16} = {( \frac{5}{4} )}^{2}$

$(m + \frac{1}{4} ) = + - \frac{5}{4}$

$m = - \frac{1}{4} + \frac{5}{4} or \: - \frac{1}{4} - \frac{5}{4}$

$m = \frac{5 - 1}{4} \: or \: - \frac{5 + 1}{4}$

$m \: = \frac{4}{4} \: or \: - \frac{6}{4}$

$m = 1 \: or \: - \frac{3}{2}$