#"rearrange the equation in "color(blue)"standard form"#
#•color(white)(x)ax^2+bx+c=0#
#rArr-4x^2+8x+3=0larrcolor(blue)"in standard form"#
#"consider the a-c method of factorising"#
#"there are no whole numbers of - 12 which sum to + 8"#
#"we can solve using the method of "color(blue)"completing the square"#
#• " the coefficient of the "x^2" term must be 1"#
#"factor out "-4#
#rArr-4(x^2-2x-3/4)=0#
#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2-2x#
#rArr-4(x^2+2(-1)xcolor(red)(+1)color(red)(-1)-3/4)=0#
#rArr-4(x-1)^2-4(-1-3/4)=0#
#rArr-4(x-1)^2+7=0#
#"subtract 7 and divide by "-4#
#rArr(x-1)^2=7/4#
#color(blue)"take the square root of both sides"#
#rArrx-1=+-sqrt(7/4)larrcolor(blue)"note plus or minus"#
#"add 1 to both sides"#
#rArrx=1+-1/2sqrt7larrcolor(red)"exact solutions"#
