Question

Which of the following is a solution of x2 + 4x = -8?

O x = -2 - 21
O x = 2 + 21
O x = -4 + 41
O x = 4 - 41

Answer 1

`x=2i-2,\:x=-2i-2`

Explanation:

`x^2 + 4x = -8\\\\\mathrm{Solve\:by\:completing\:the\:square}\\\\\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2\\\\\mathrm{Solve\:for\:}a,\:2ax=4x:\quad a=2\\\\\mathrm{Add\:}a^2=2^2\mathrm{\:to\:both\:sides}\\\\x^2+4x+2^2=-8+2^2\\\\\mathrm{Simplify\:}-8+2^2:\quad -4\\x^2+4x+2^2=-4\\\\\mathrm{Complete\:the\:square}\\\left(x+2\right)^2=-4\\\\\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=√(a),\:-√(a)\\`

`\mathrm{Solve\:}\:x+2=√(-4):\quad x=2i-2\\\\\mathrm{Solve\:}\:x+2=-√(-4):\quad x=-2i-2\\\\x=2i-2,\:x=-2i-2\\`