Question

Solve this equation by completing the square.

3x2 - 4x = -2

Answer 1

\[\huge 3x^2 - 4x = -2 \]
dividing both sides by 3 we find:
\[\huge x^2 - \frac{4}{3}x = \frac{-2}{3} \]
\[\huge \rightarrow x^2 -2 \times \frac{2}{3}x = \frac{-2}{3} \]
Now it is clear that we have to add the square of (2/3) both sides hence we find:
\[\huge \rightarrow x^2 -2 \times \frac{2}{3}x +(\frac{2}{3})^2= \frac{-2}{3} +(\frac{2}{3})^2\]
\[\huge \rightarrow x^2 -2 \times \frac{2}{3}x +(\frac{2}{3})^2= \frac{-2}{3} +\frac{4}{9}\]
\[\huge \rightarrow [x-(\frac{2}{3})]^2= \frac{-6}{9} +\frac{4}{9}\]
\[\huge \rightarrow [x-(\frac{2}{3})]^2= \frac{-2}{9} \]
Now work it out further.

Answer 2

3x^2 - 4x = -2
you can use delta