Answer:
The given equation is of the form
p( x+ q)² + r = [tex]3((x+(-\frac{7}{6})^{2} +(-\frac{61}{12})[/tex]
Step-by-step explanation:
Step(i):-
Given equation 3 x² - 7 x -1
= [tex]3(x^{2} -\frac{7}{3} x )-1[/tex]
= [tex]3(x^{2} -2 X \frac{7}{3X2} +(\frac{7}{6} )^{2}-(\frac{7}{6} ^{2} )-1[/tex]
= [tex]3(x^{2} -2 X \frac{7}{6} +(\frac{7}{6} )^{2}-(\frac{49}{36} )) -1[/tex]
Step(ii):-
We know that formula
(a-b)² = a² - 2ab + b²
[tex]3x^{2} -7x-1 = 3((x-\frac{7}{6})^{2} -( 3X\frac{49}{36} )) -1[/tex]
[tex]3x^{2} -7x-1 = 3((x-\frac{7}{6})^{2} -\frac{61}{12}[/tex]
Final answer:-
The given equation is of the form
p( x+ q)² + r = [tex]3((x+(-\frac{7}{6})^{2} +(-\frac{61}{12})[/tex]
