Question

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

A) x=-4

B) x=-2

C) x=2

D) x=4

Answer 1

`2 {x}^(2) + 8x = {x}^(2) - 16 \\ 2 {x}^(2) - {x}^(2) + 8x + 16 = 0 \\ {x}^(2) + 8x + 16 = 0 \\ (x + 4)(x + 4) = 0 \\ x + 4 = 0 \: \: \: \: \: \: \: or \: \ \: \: \: \: \: \:x + 4 = 0 \\ x = - 4`

Hope it helps

Answer 2

Given:
`2x^2+8x=x^2-16`

Find: The value of the unknown, x

Solution: The first step that we need to take is to subtract
`x^2` from both sides and then add 16 from both sides. After that we need to factor out the expression and then solve for x.

Subtract
`x^2` from both sides

• 
  `2x^2 - x^2+8x=x^2 - x^2-16`

• 
  `x^2+8x = -16`

Add 16 to both sides

• 
  `x^2+8x + 16 = -16 + 16`

• 
  `x^2+8x + 16 = 0`

Factor our the expression

• 
  `x^2+8x + 16 = 0`

• 
  `(x + 4)^2 = 0`

Solve for x

• 
  `x + 4 = 0`

• 
  `x + 4 - 4 = 0 - 4`

• 
  `x = 0 - 4`

• 
  `x = - 4`

Now that we have fully expanded the expression and determine the value of the unknown we can say that the correct answer would be option A, x = -4.