Question

Solve the equation 6x2 + x – 2 = 0 by method of completing square.

Answer 1

first divide eqn by 6
x^2+x/6-1/3=0
then add and subtract 1/144
x^2+2*x*1/12+1/144-1/144-1/3=0
(x+1/12)^2-49/144=0
then transpose-49/144 to other side
(x+1/12)^2=49/144
taking square root on both sides
x+1/12=+-7/12
x=1/2,-2/3

Answer 2

Given :

6 x² + x - 2 = 0

Divide both sides by co-effecient of the first term !

( 6 x² + x - 2 ) / 6 = 0/6

==> x² + x / 6 - 2 / 6 = 0

==> x² + 2 × x × 1 / 12 - 1 / 3 = 0

Now we have to add (1/12)² both sides :

==> x² + 2 × x × 1/12 - 1/3 + (1/12)² = (1/12)²

Use the formula : a² + 2 × a × b + b² = ( a + b )²

==> ( x + 1/12 )² - 1/3 = 1/144

==> ( x + 1/12 )² = 1/144 + 1/3

==> ( x + 1/12 )² = ( 1 + 48 ) / 144

==> ( x + 1/12 )² = 49/144

==> ( x + 1/12 )² = (7/12)²

Take square roots both sides :

==> x + 1/12 = ± 7/12

==> x = ± 7/12 - 1/12

Either

==> x = 7/12 - 1/12

==> x = 6/12

==> x = 1/2

or :

x = -7/12 - 1/12

==> x = -8/12

==> x = -2/3

ANSWERS :

x = 1/2

x = -2/3

Hope it helps :-)

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