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Question 1121300: Resuelve factorizando la ecuacion: 0=ื^2-3ื-108
(Mas entendible: 0=ืal cuadrado-3ื-108
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the quadratic equation is x^2 - 3x - 108 = 0
108 / 2 = 54
54 - 2 is not equal to 3.
108 / 3 = 36
36 - 3 is not equal to 3.
108 / 6 = 18
18 - 6 is not equal to 3
108 / 9 = 12
12 - 9 is equal to 3, therefore this combination should work.
since the constant term is negative, then it's going to be 12 * -9 or it's going to be 9 * -12.
either one will get you -108.
since the middle term is negative, then it can't be 12 - 3 becausee that's positive.
it has to be 9 - 12 = -3.
therefore the factors have to be (x - 12) * (x + 9).
when you multiply these factors out, you get:
(x - 12) * (x + 9) = x^2 + 9x - 12x - 108
combine like terms to get x^2 - 3x - 108.
either one of the factors have to be equal to 0, or both have to be equal to 0.
when x - 12 = 0, solve for x to get x = 12.
when x + 9 = 0, solve for x to get x = -9
if the values of x are good, then x^2 - 3x - 108 should be equal to 0 when you replace x with either 12 or -9.
when x = 12, x^2 - 3x - 108 = 12^2 - 3*12 - 108 = 144 - 36 - 108 = 0.
when x = -9, x^2 - 3x - 108 = (-9)^2 -3*-9 - 108 = 81 + 27 - 108 = 0.
both solutions are good.
not sure if that's what you want, but that's what you get.
here's what the solution looks like on a graph.
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
For numerous examples on how to solve quadratic equations using factorization method, see the lesson
- Solving quadratic equations without quadratic formula
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this textbook under the topic "Quadratic equations".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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