Question 1027958: 4x^2+16x+12=0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! start with 4x^2 + 16x + 12 = 0.
multiply the coefficient of the x^t term by the constant term to get 4 * 12 = 48
if the factors add up to 16, then you have your factors and you can split the middle term into 4x + 12x = 16x.
your expression becomes 4x^2 + 4x + 12x + 12 = 0
group the first 2 terms togetherand group the last 2 terms together.
your expression becomes (4x^2 + 4x) + (12x + 12) = 0
take out the gcf from each of the grouped terms to get:
4x * (x+1) + 12 * (x+1) = 0
take out the common factor to get:
(4x+12) * (x+1) = 0
those are your factors.
solve for x to get:
x = -3 or x = -1
replace x with each of these values and the result should be 0 = 0.
when x = -3, 4x^2 + 16x + 12 becomes 36 - 48 + 12 = 0 which becomes 0 = 0.
when x = -1, 4x^2 + 16x + 12 becomes 4 - 16 + 12 = 0 which becomes 0 = 0.
the solution looks.
x = -3 or x = -1.
you could also have used the quadratic formula.
the quadratic formula will solve any quadratic equation, regardless if the roots are real or complex (real and imaginary part).
if you need a tutorial on how to favctor a quadratic, here's one that's pretty good.
http://www.purplemath.com/modules/factquad.htm
here's another that uses the method i just used.
http://www.regentsprep.org/regents/math/algtrig/atv1/revFactorGrouping.htm
here's yet another that uses the box method.
http://www.regentsprep.org/regents/math/algtrig/atv1/LgroupingBox.htm
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