Question

Which of the following methods would be the easiest to use to solve 12x2 – 48 = 0?



isolating the x2 term and finding the square root of both sides

All three methods would be easy and effective.

using the quadratic formula

factoring

Answer 1

$\bf \stackrel{\textit{solving for \underline{x}}}{12x^2-48=0\implies 12x^2=48\implies x^2=\cfrac{48}{12}\implies x^2=4} \\\\\\ x=\pm\sqrt{4}\implies x=\pm 2$

Answer 2

All three methods are easy and effective. Here's solving the equation using all three methods.

First Option:

$12x^2-48=0\\ 12x^2=48\\ x^2=4\\ x=+/-\sqrt{4} \\ x=2,-2$

Third Option (Remember that the equation for the quadratic formula is $x=\frac{-b+\sqrt{b^2-4ac}}{2a},\frac{-b-\sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant):

$x=\frac{-0+\sqrt{0^2-4*12*(-48)}}{2*12},\frac{-0-\sqrt{0^2-4*12*(-48)}}{2*12}\\\\ x=\frac{-0+\sqrt{2304}}{24},\frac{-0-\sqrt{2304}}{24}\\ \\ x=\frac{48}{24},\frac{-48}{24}\\\\ x=2,-2$

Fourth Option:

$12x^2-48=0\\12(x^2-4)=0 \\ 12(x+2)(x-2)=0\\ \\ x+2=0\\ x=-2\\ \\ x-2=0\\ x=2$