help w/ solving by completing the square: x^2 + 4x + 3 = 0

[emdorsheimer]

These are getting harder because this is a college trying to jam a years worth of schooling into a nine week period.

Solve by completing the square: x^2 + 4x + 3 = 0

Please help with the steps. thanks

 

[stapel]

I'll demonstrate the steps using a different equation:

Quadratic equation:

. . . . .3x² + 6x - 5 = 0

Put any constant terms on the other side:

. . . . .3x² + 6x = 5

Factor out whatever is multiplied on the square term (if anything):

. . . . .3(x² + 2x) = 5

Find half of the coefficient on the linear term:

. . . . .(1/2)(2) = 1

Square, and add to both sides, taking account of the factoring:

. . . . .3(x² + 2x + 1) = 5 + 3(1)

Simplify into perfect-square form:

. . . . .3(x + 1)² = 8

. . . . .(x + 1)² = 8/3

Solve:

. . . . .x + 1 = ± sqrt[8/3]

Simplify as appropriate to obtain the final answer.

Eliz.