"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"
