"simplify by collecting like terms"simplify by collecting like terms
rArrx^2+12x+12x+11⇒x2+12x+12x+11
=x^2+24x+11=x2+24x+11
"this does not factor with integer coefficients so"this does not factor with integer coefficients so
"find the roots using the "color(blue)"quadratic formula"find the roots using the quadratic formula
x^2+24x+11=0x2+24x+11=0
"with "a=1,b=24,c=11with a=1,b=24,c=11
rArrx=(-24+-sqrt(24^2-(4xx1xx11)))/2⇒x=−24±√242−(4×1×11)2
color(white)(rArrx)=(-24+-sqrt(576-44))/2⇒x=−24±√576−442
color(white)(rArrx)=(-24+-sqrt532)/2⇒x=−24±√5322
color(white)(rArrx)=(-24+-2sqrt133)/2=-12+-sqrt133⇒x=−24±2√1332=−12±√133
rArrx^2+24x+11⇒x2+24x+11
=(x-(-12+sqrt133))(x-(-12-sqrt133))=(x−(−12+√133))(x−(−12−√133))
=(x+12-sqrt133)(x+12+sqrt133)=(x+12−√133)(x+12+√133)
