Question

Solve : 0 = 13x^2 + 20x - 92

Answer 1

13x2-20x-92=0 

Two solutions were found :

 x = -2 x = 46/13 = 3.538

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(13x2 - 20x) - 92 = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  13x2-20x-92 

The first term is,  13x2  its coefficient is  13 .
The middle term is,  -20x  its coefficient is  -20 .
The last term, "the constant", is  -92 

Step-1 : Multiply the coefficient of the first term by the constant   13 • -92 = -1196 

Step-2 : Find two factors of  -1196  whose sum equals the coefficient of the middle term, which is   -20 .

     -1196   +   1   =   -1195     -598   +   2   =   -596     -299   +   4   =   -295     -92   +   13   =   -79     -52   +   23   =   -29     -46   +   26   =   -20   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -46  and  26 
                     13x2 - 46x + 26x - 92

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (13x-46)
              Add up the last 2 terms, pulling out common factors :
                    2 • (13x-46)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (13x-46)
             Which is the desired factorization

Equation at the end of step  2  :

(13x - 46) • (x + 2) = 0

Answer 2

Answer:

CLASS 10TH

{if you are from ICSE board then this question is for 10th class not for 9th if you are in 9th, I can do both in 9th and 10th method}

solution:

CLASS 9TH

0=13x²+20x-92

0=13x²+(46-26)x-92

0=13x²+46x-26x-92

0=x(13x+46)-2(13x+46) [common factor from 2 pairs]

now,rewrite in factored form:

0=x(13x+46)-2(13x+46)

0=(x- 2)(13x+46x)

x=2 , 46/13