How do I complete the square if $f(x) = 3x^2 + 12x - 9$ ?

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Answer 1 · 2014-09-13T22:42:17

Begin by adding 9 to both sides of the equation.

$3x^2+12x=9$

Factor out a $3$ from the left side of the equation.

$3(x^2+4x)=9$

Locate the $x$ term and take half of the coefficient and square it

$(4/2)^2=2^2=4$

Add $3*4$ to the right side of the equation. Because we factored out a $3$ .

On the left side add $4$ within the parenthesis.

$3(x^2+4x+4)=9+12$ , Perfect square trinomial

$3(x+2)^2=9+12$

$3(x+2)^2=21$

$(x+2)^2=7$ , Divide by 3

$sqrt((x+2)^2)=sqrt(7)$

$x+2=+-sqrt(7)$

$x=+-sqrt(7)-2$

How do I complete the square if f(x) = 3x^2 + 12x - 9f(x) = 3x^2 + 12x - 9?