Question

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

Answer 1

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

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.

Answer 2

`x=-4`

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`