SOLUTION: Solve by two methods, quadratic equation and factoring: 2x^2-x-15=0

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Question 1038879: Solve by two methods, quadratic equation and factoring:
2x^2-x-15=0

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve by two methods, quadratic equation and factoring:
2x^2-x-15=0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As I just said in https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1038843.html,
solve on your own at least by the quadratic formula.

Demonstrate that you can do this arithmetic.

Comment from student:
Solve by 2 methods,Quad Equation and Factoring : 2x^2-x-15=0 
You ask me to show, this may or may not be right 

X=-b±√b^2-4ac/2a. a=2, b= -1, c= -15 X=-(-1)±√1^2+4^2(-15)/2^2 X1,2=(1±11)/2^2 X1=12/4= 3 X2=-10/4= -5/2 

Having problems with getting my zero Factoring right and checking problem 


My responce: Bravo that you found a courage to start it.

Your calculations are incorrect, and I see that you really need help. Let me fix it:

X = %281+%2B-+sqrt%28%28-1%29%5E2+-+4%2A2%2A%28-15%29%29%29%2F4 = %281+%2B-+sqrt%281+%2B+120%29%29%2F4 = %281+%2B-+sqrt%28121%29%29%2F4 = %281+%2B-+11%29%2F4.

x%5B1%5D = 12%2F4 = 3,  x%5B2%5D = -10%2F4 = -5%2F2.

Now factoring:

2x%5E2-x-15 = 2%2A%28x-x%5B1%5D%29%2A%28x-x%5B2%5D%29 = 2%2A%28x+-+3%29%2A%28x-%28-5%2F2%29%29 = %28x-3%29%2A%282x%2B5%29.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by two methods, quadratic equation and factoring:
2x^2-x-15=0
I would use the factoring method 1st, since it's easier, and you can use the solution(s) to check the solution(s) after using
the quadratic equation formula
2x%5E2+-+x+-+15+=+0
2x%5E2+-+6x+%2B+5x+-+15+=+0 ------- Replacing - x with - 6x + 5x
2x%28x+-+3%29+%2B+5%28x+-+3%29+=+0
%282x+%2B+5%29%28x+-+3%29+=+0+
2x + 5 = 0 OR x - 3 = 0
highlight_green%28matrix%281%2C3%2C+x+=+-+5%2F2%2C+or%2C+x+=+3%29%29