Question

−7x = x2 + 12

Answer 1

-7x = x2 + 12

x2 + 7x + 12 = 0

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

x+3=0, x+4=0

x= -3, x= -4

Answer 2

Answer:

It appears that the answer is D.

Step-by-step explanation:

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

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

And so that is why the answer is D.