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199932

[tex]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[/tex]

Hope it helps

igoroleshko156

Given: [tex]2x^2+8x=x^2-16[/tex]

Find:  The value of the unknown, x

Solution: The first step that we need to take is to subtract [tex]x^2[/tex] 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 [tex]x^2[/tex] from both sides

  • [tex]2x^2 - x^2+8x=x^2 - x^2-16[/tex]
  • [tex]x^2+8x = -16[/tex]

Add 16 to both sides

  • [tex]x^2+8x + 16 = -16 + 16[/tex]
  • [tex]x^2+8x + 16 = 0[/tex]

Factor our the expression

  • [tex]x^2+8x + 16 = 0[/tex]
  • [tex](x + 4)^2 = 0[/tex]

Solve for x

  • [tex]x + 4 = 0[/tex]
  • [tex]x + 4 - 4 = 0 - 4[/tex]
  • [tex]x = 0 - 4[/tex]
  • [tex]x = - 4[/tex]

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.

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