"to use the method of "color(blue)"completing the square"to use the method of completing the square
• " the coefficient of the "x^2" term must be 1"∙ the coefficient of the x2 term must be 1
rArr2(x^2-7/2x-15/2)=0⇒2(x2−72x−152)=0
• " add/subtract "(1/2"coefficient of the x-term")^2" to"∙ add/subtract (12coefficient of the x-term)2 to
x^2-7/2xx2−72x
2(x^2+2(-7/4)xcolor(red)(+49/16)color(red)(-49/16)-15/2)=02(x2+2(−74)x+4916−4916−152)=0
rArr2(x-7/4)^2+2(-49/16-15/2)=0⇒2(x−74)2+2(−4916−152)=0
rArr2(x-7/4)^2-169/8=0⇒2(x−74)2−1698=0
rArr2(x-7/4)^2=169/8⇒2(x−74)2=1698
rArr(x-7/4)^2=169/16⇒(x−74)2=16916
color(blue)"take the square root of both sides"take the square root of both sides
rArrx-7/4=+-sqrt(169/16)larrcolor(blue)"note plus or minus"⇒x−74=±√16916←note plus or minus
rArrx=7/4+-13/4⇒x=74±134
rArrx=7/4-13/4=-3/2" or "x=7/4+13/4=5⇒x=74−134=−32 or x=74+134=5
