Question

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Answer 1

The given equation is of the form

p( x+ q)² + r =
`3((x+(-(7)/(6))^(2) +(-(61)/(12))`

Explanation:

Step(i):-

Given equation 3 x² - 7 x -1

=
`3(x^(2) -(7)/(3) x )-1`

=
`3(x^(2) -2 X (7)/(3X2) +((7)/(6) )^(2)-((7)/(6) ^(2) )-1`

=
`3(x^(2) -2 X (7)/(6) +((7)/(6) )^(2)-((49)/(36) )) -1`

Step(ii):-

We know that formula

(a-b)² = a² - 2ab + b²

`3x^(2) -7x-1 = 3((x-(7)/(6))^(2) -( 3X(49)/(36) )) -1`

`3x^(2) -7x-1 = 3((x-(7)/(6))^(2) -(61)/(12)`

Final answer:-

The given equation is of the form

p( x+ q)² + r =
`3((x+(-(7)/(6))^(2) +(-(61)/(12))`