by completing the square .sh ) y=3x^2-12x+4

## Step 1: Rewrite the equation<br />### Move the constant term to the right side of the equation.<br />$3x^2 - 12x = -4$<br /><br />## Step 2: Factor out the coefficient of the $x^2$ term<br />### Factor out 3 from the left side.<br />$3(x^2 - 4x) = -4$<br /><br />## Step 3: Complete the square<br />### Divide the coefficient of the $x$ term by 2 and square it: $(\frac{-4}{2})^2 = 4$. Add this inside the parenthesis, and add 3 times this value (since we factored out a 3) to the right side to maintain balance.<br />$3(x^2 - 4x + 4) = -4 + 3(4)$<br />$3(x^2 - 4x + 4) = -4 + 12$<br />$3(x^2 - 4x + 4) = 8$<br /><br />## Step 4: Rewrite as a perfect square<br />### Rewrite the left side as a perfect square.<br />$3(x-2)^2 = 8$<br /><br />## Step 5: Solve for x<br />### Divide both sides by 3, then take the square root of both sides.<br />$(x-2)^2 = \frac{8}{3}$<br />$x-2 = \pm\sqrt{\frac{8}{3}}$<br />$x = 2 \pm\sqrt{\frac{8}{3}}$<br />$x = 2 \pm\frac{2\sqrt{6}}{3}$