Question

30 POINTS PLEASE HELP2 QUESTIONS

Answer 1

x^2 + 14x = 32

To make a perfect square, you need to add 49 to both sides

x^2 + 14x + 49 = 32 + 49

Answer:  49

Solve:

x^2 + 14x + 49 = 32 + 49

(x + 7)^2 = 81

(x + 7)^2 = 9^2

So

x + 7 = 9

x = 2

and

x + 7 = -9

x = -16

Answer:

x = 2 and x = -16

Answer 2

Answer:

2 and -16

Step-by-step explanation:

https://www.tiger-algebra.com/drill/x~2_14x=32/

"Two solutions were found :

x = 2

x = -16

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^2+14*x-(32)=0

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2+14x-32

The first term is,  x2  its coefficient is  1 .

The middle term is,  +14x  its coefficient is  14 .

The last term, "the constant", is  -32

Step-1 : Multiply the coefficient of the first term by the constant   1 • -32 = -32

Step-2 : Find two factors of  -32  whose sum equals the coefficient of the middle term, which is   14 .

     -32    +    1    =    -31

     -16    +    2    =    -14

     -8    +    4    =    -4

     -4    +    8    =    4

     -2    +    16    =    14    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  16

                    x2 - 2x + 16x - 32

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

                   x • (x-2)

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

                   16 • (x-2)

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

                   (x+16)  •  (x-2)

            Which is the desired factorization

Equation at the end of step  1  :

 (x + 16) • (x - 2)  = 0 "