Question

40 Use the method of completing the square to transform the quadratic equation into the equation form (x -p2-q. ?9 + 12x-6x2 =0 A) (x-1)2??0.5 B) 12- -1.5 C) D) (1)2-1.5 (x-1)2-0.5

Answer 1

Given equation is-
$\small -9+12x-6x^2=0$

Divide both sides by $\small -6$
$\small =>\frac{-9+12x-6x^2}{-6}=0$
$\small =>\frac{-9}{-6}+\frac{12x}{-6}-\frac{6x^2}{-6}=0$
$\small =>\frac{3}{2}-2x+x^2=0$

rearanging-
$\small =>x^2-2x+\frac{3}{2}=0$

Split the term $\tiny \frac{3}{2}=\frac{2+1}{2}$
$\small =>x^2-2x+\frac{2+1}{2}=0$
$\small =>x^2-2x+\frac{2}{2}+\frac{1}{2}=0$
$\small =>x^2-2x+1+\frac{1}{2}=0$

As we know $\small (a-b)^2=a^2-2ab+b^2$
$\small =>x^2-2x+1^2+\frac{1}{2}=0$ (as we know 1²=1)
$\small =>(x-1)^2+\frac{1}{2}=0$

Subtract both sides by $\tiny \frac{1}{2}$
$\small =>(x-1)^2+\frac{1}{2}-\frac{1}{2}=-\frac{1}{2}$
$\small =>(x-1)^2=-\frac{1}{2}$
$\small =>(x-1)^2=-0.5$

Hence answer is-
$\small A)\quad (x-1)^2=-0.5$