Solve |3x+1| = 1
Firstly square both sides. This way, we now know that both sides have to be positive
(3x+1)^2 = 1
(3x+1)(3x+1) = 1
Expand the quadratic...
9x^2 + 12x + 4 = 1
9x^2 + 12x + 3 = 0
Now complete the square. Firstly divide everything by 12 to make this simpler
x^2 + (4/3)x + 1/3 = 0
(x + (2/3))^2 -4/9 + 1/3 = 0
(x + (2/3))^2 = 1/9
Square root both sides, be sure to have give the negative value on RHS too
x+(2/3)=+-(1/3)
x=-1/3 x=-1
DT
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