Solve the following incomplete quadratic equations:
1) $$3x^2-12=0$$
2) $$x^2-x=0$$
3) $$1-4x^2=-8$$
Development:
1) Since there is only one term with $$x$$, we can isolate the unknown directly: $$$3x^2-12=0$$$ $$$3x^2=12$$$ $$$x^2=\dfrac{12}{3}=4$$$ $$$x=\pm\sqrt{4}=\pm2$$$ $$$x_1=2 \ \text{and} \ x_2=-2$$$
2) Since there is no independent term, we can take the common factor of the $$x$$: $$$x^2-x=0$$$ $$$x(x-1)=0$$$ $$$x_1=0; \ \text{and} \ x-1=0\rightarrow x_2=1$$$
3) Since there is only one term with $$x$$, we can isolate the unknown directly: $$$1-4x^2=-8$$$ $$$1+8=4x^2$$$ $$$\dfrac{9}{4}=x^2$$$ $$$x=\dfrac{\pm\sqrt{9}}{\pm\sqrt{4}}=\dfrac{\pm3}{\pm2}$$$ $$$x_1=\dfrac{3}{2} \ \text{and} \ x_2=\dfrac{-3}{2}$$$
Solution:
1) $$x_1=2 \ \text{and} \ x_2=-2$$
2) $$x_1=0 \ \text{and} \ x_2=1$$
3) $$x_1=\dfrac{3}{2} \ \text{and} \ x_2=\dfrac{-3}{2}$$