Question

Solve 3x2 − 24x = −12.

A) 4 ± 2square root 2
B) 4 ± 2square root 3
C) 4 ± 2square root 5
D) 4 ± 2square root 7

Answer 1

B) 4 ± 2square root 3

Explanation:

`3x^2-24x=-12\qquad\text{divide both sides by 3}\\\\x^2-8x=-4\\\\x^2-2(x)(4)=-4\qquad\text{add}\ 4^2\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=-4+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=-4+16\\\\(x-4)^2=12\to x-4=\pm√(12)\\\\x-4=\pm√(4\cdot3)\\\\x-4=\pm\sqrt4\cdot\sqrt3\\\\x-4=\pm2\sqrt3\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt3`