SOLUTION: what is the step by step solution to w(2w+1)=15 and how do I discover what the width is

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Question 1193299: what is the step by step solution to w(2w+1)=15 and how do I discover what the width is
Found 3 solutions by MathLover1, josgarithmetic, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

w%282w%2B1%29=15.....first multiply
w%2A2w%2Bw%2A1=15
2w%5E2%2Bw=15
2w%5E2%2Bw-15=0........factor, write w as 6w-5w
2w%5E2%2B6w-5w-15=0....group
%282w%5E2%2B6w%29-%285w%2B15%29=0
2w%28w%2B3%29-5%28w%2B3%29=0
%28w+%2B+3%29%282w+-+5%29+=+0
solutions:
if %28w+%2B+3%29+=+0 =>w=-3
if %282w+-+5%29+=+0 =>w=5%2F2


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is just a re-wording of your other posting.
Already solved there.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.


            Here is the way to solve the problem  MENTALLY. 


Take your original equation

    w*(2w+1) = 15


and multiply both sides by 2.  You will get an EQUIVALENT equation

    2w*(2w+1) = 30.
    

Now ask yourself, which two consecutive numbers, 2w and 2w+1 make the product of 30.


One guess is obvious: the numbers are 5 and 6.
Hence, 2w = 5,  which gives  w = 5/2 = 2.5.


    Another guess  is -5 and -6, 
    which gives  2w+1 = -5,   2w = -6,   w = -3.

Solved.