Question

What is the solution to 2x2+8x=x2-16?

Answer 1

Answer:

x = -4

Step-by-step explanation:

=> 2x²+8x = x²-16

=> 2x²- x² + 8x + 16 = 0

=> x² + 8x + 16 = 0

Using mid-term break formula

=> x² + 4x + 4x + 16 = 0

=> x(x+4)+4(x+4) = 0

=> (x+4)(x+4) = 0

=> (x+4)² = 0

Taking square root on both sides

=> x+4 = 0

=> x = -4

Answer 2

Answer:

x = -4

Step-by-step explanation:

1. (2x2 +  8x) -  (x2 - 16)  = 0

2. Factoring  x2+8x+16  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +16  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16  

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   8 .

     -16    +    -1    =    -17  

     -8    +    -2    =    -10  

     -4    +    -4    =    -8  

     -2    +    -8    =    -10  

     -1    +    -16    =    -17  

     1    +    16    =    17  

     2    +    8    =    10  

     4    +    4    =    8    That's it

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

                    x2 + 4x + 4x + 16

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

                   x • (x+4)

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

                   4 • (x+4)

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

                   (x+4)  •  (x+4)

            Which is the desired factorization

Multiply  (x+4)  by  (x+4)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+4)  and the exponents are :

         1 , as  (x+4)  is the same number as  (x+4)1  

and   1 , as  (x+4)  is the same number as  (x+4)1  

The product is therefore,  (x+4)(1+1) = (x+4)2

(x + 4)2  = 0

3.

Solve  :    (x+4)2 = 0  

 (x+4) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means :   x+4  = 0

Subtract  4  from both sides of the equation :  

                     x = -4