Question

−7x = x2 + 12

A) x = 3, x = 5
B) x = 3, x = 4
C) x = −3, x = 5
Eliminate
D) x = −4, x = −3

Answer 1

It appears that the answer is D.

Explanation:

`Steps\\$-7x=2x+12$\\\\$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}:$\\-7x-2x=2x+12-2x\\\\\\\mathrm{Simplify}:\\-9x=12\\\\\mathrm{Divide\:both\:sides\:by\:}-9:\\(-9x)/(-9)=(12)/(-9)\\\\\mathrm{Simplify}:\\(-9x)/(-9)=(12)/(-9)\\\\\mathrm{Part\ one:Simplify\:}(-9x)/(-9):\quad x\\\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(-b)=(a)/(b)\\=(9x)/(9)\\\\\mathrm{Divide\:the\:numbers:}\:(9)/(9)=1\\=x`

`\mathrm{Part\ two:Simplify\:}(12)/(-9):\quad -(4)/(3)\\\\\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)\\=-(12)/(9)\\\\\mathrm{Cancel\:the\:common\:factor:}\:3\\=-(4)/(3)\\\\x=-(4)/(3)\\`

And so that is why the answer is D.

Answer 2

-7x = x2 + 12

x2 + 7x + 12 = 0

(x+3)(x+4)=0

x+3=0, x+4=0

x= -3, x= -4