Question

what constant number must be added or subtracted to 4x^2 + 12x + 8=0 to solve it by the method of completing the square

Answer 1

$4 {x}^{2} + 12x + 8 = 0$

$4 {x}^{2} + 12x = - 8$
dividing throughout by 4

${x}^{2} + 3x = - 2..............(1)$
third term that should be added
$( { \frac{1}{2 } \times coefficient \: x })^{2}$

$= ( { \frac{1}{2} \times 3)}^{2}$
$= ( {\frac{3}{2} )}^{2}$

$= \frac{9}{4}$
Therefore,
the constant number that should be added to
$4 {x}^{2} + 12x + 8 = 0$
to solve by completing square method is :
$\frac{9}{4} .$
$hope \: this \: \: helps$