Question

What is the only solution for 2x to the second power + 8x equals x to the second power - 16

Answer 1

Answer:

$x=-4$

Step-by-step explanation:

we are given equation as

$2x^2+8x=x^2-16$

Since, we have to solve for x

so, we will make all terms on left side

add both sides 16

$2x^2+8x+16=x^2-16+16$

$2x^2+8x+16=x^2$

Subtract both sides by x^2

$2x^2+8x+16-x^2=x^2-x^2$

$x^2+8x+16=0$

now, we can factor it

$(x+4)^2=0$

now, we can solve for x

and we get

$x=-4$

Answer 2

Answer:

The only solution of given equation is x=-4.

Step-by-step explanation:

The given equation is

$2x^2+8x=x^2-16$

$2x^2+8x-x^2+16=0$

$x^2+8x+16=0$

$x^2+2(x)(4)+4^2=0$

$(x+4)^2=0$                       $\because (a+b)^2=a^2+2ab+b^2$

$(x+4)=0$

$x=-4$

Therefore the only solution of given equation is x=-4.