Question

Solve : $3(x+2{)}^2-32=48-2(x+2{)}^2$

• A. $x=2,6$
• B. $x=-2,6$
• C. $x=2,-6$
• D. $x=-2,-6$

Answer 1

The correct option is C $x=2,-6$

The given equation $3{(x+2)}^2-32=48-2{(x+2)}^2$ can be solved as shown below:

$3{(x+2)}^2-32=48-2{(x+2)}^2\Rightarrow 3[x^2+2^2+(2\times x\times 2\left)\right]-32=48-2[x^2+2^2+(2\times x\times 2\left)\right](\because {(a+b)}^2=a^2+b^2+2ab)\Rightarrow 3\left(x^2+4+4x\right)-32=48-2\left(x^2+4+4x\right)\Rightarrow 3x^2+12+12x-32=48-2x^2-8-8x\Rightarrow 3x^2+12x-20=-2x^2-8x+40\Rightarrow 3x^2+2x^2+12x+8x-20-40=0\Rightarrow 5x^2+20x-60=0\Rightarrow x^2+4x-12=0$

$\Rightarrow x^2+6x-2x-12=0\Rightarrow x(x+6)-2(x+6)=0\Rightarrow (x-2)(x+6)=0\Rightarrow (x-2)=0,(x+6)=0\Rightarrow x=2,x=-6$

Hence, $x=2,-6$.