How do you solve using the completing the square method 3x^2-6x-1=0?

1 Answer
EZ as pi
Dec 26, 2016

x=2.155" or "x = -0.155

Explanation:

Quadratic equations are in the form ax^2 +bx+c =0

color(lime)(3)x^2 -6x-1=0" "larrdiv 3 to make color(lime)(a=1)
color(lime)(darr)
color(lime)(1)x^2 -2x-1/3 =0" "larr move -1/3 to the RHS

x^2 -2x" "=1/3

x^2 -2x color(blue)(+ square) = +1/3" "larrcolor(blue)( square= (b/2)^2)
color(white)(.......)color(blue)(darr)
" "color(blue)(((-2)/2)^2 = 1= square)" "larr add to both sides

x^2 -2x color(blue)(+1) = +1/3color(blue)(+1)" "larrthis is completing the square

[Now use the identity color(red)(a^2 + 2ab+b^2 = (a+b)^2) ]

color(red)(x^2 -2x +1) = +1 1/3
color(white)(....)color(red)(darr)
color(red)((x-1)^2) = 1 1/3 =4/3" "find square root both sides

x-1 = +-sqrt(4/3)" "larr solve for x twice

x = +sqrt(4/3) +1" and "x = -sqrt(4/3)+1

x =2/sqrt3 +1" and "x = (-2)/sqrt3 +1

x=2.155" or "x = -0.155

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