Solve by factoring x^2 -9x-52=0

x=13, x=-4

Step-by-step explanation:

please :))

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-9x-52

The first term is,  x2  its coefficient is  1 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -52

Step-1 : Multiply the coefficient of the first term by the constant   1 • -52 = -52

Step-2 : Find two factors of  -52  whose sum equals the coefficient of the middle term, which is   -9 .

     -52     +    1     =    -51  

     -26     +    2     =    -24  

     -13     +    4     =    -9     That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -13  and  4

                    x2 - 13x + 4x - 52

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-13)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-13)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-13)

            Which is the desired factorization

 (x + 4) • (x - 13)  = 0

-4, 13

Step-by-step explanation:

x²-9x-52=0

Delta=(-9)²-4×1×(-52)=81+208=289=17²

x1=(-(-9)+sqrt(delta))/2=(9+17)/2=26/2=13

x2=(-(-9)-sqrt(delta))/2=(9-17)/2=-8/2=-4

So:

x²-8x-52=(x-13)(x+4)=0

Solutions: x=13 and -4

; )

step-by-step explanation: ; )