**Question 1: **Using Completing the square method solve the equation $3x^{2}+ 2x +9 = 0$

** Solution: **

The coefficient of x^{2} is 3. Divide each term by 3 on both sides.

$x^{2}$ + $\frac{2}{3}$ x + 3 = 0

Move the constant to the right hand side.

$x^{2}$ + $\frac{2}{3}$ x = -3

Half the x- term coefficient, square it and add this value to both sides.

x-term coefficient = $\frac{2}{3}$

Half the x-term coefficient = $\frac{1}{3}$

After Squaring = $\frac{1}{9}$

Add this value to both sides

$x^{2}$ + $\frac{2}{3}$x + $\frac{1}{9}$ = -3 + $\frac{1}{9}$

Simplifying the above

$x^{2}$ + $\frac{2}{3}$x + $\frac{1}{9}$ = -$\frac{26}{9}$

The left side of the expression should be converted to perfect square and by taking square root on both sides

(x+$\frac{1}{3})^{2}$ = -$\frac{26}{9}$

x+$\frac{1}{3}$= $\pm\sqrt{\frac{-26}{9}}$

Solve for x:

x=-$\frac{1}{3}$$\pm\sqrt{\frac{-26}{9}}$

$x_{1}$ = -$\frac{1}{3}$ + $\frac{1}{3}\sqrt{26i}$

$x_{2}$ = -$\frac{1}{3}$ - $\frac{1}{3}\sqrt{26i}$

**Question 2: **Using Completing the square method solve the equation $9x^{2}- 7x -9 = 0$

** Solution: **

The coefficient of x^{2} is 9. Divide each term by 9 on both sides.

$x^{2}$ - $\frac{7}{9}$ x - 1 = 0

Move the constant to the right hand side.

$x^{2}$ - $\frac{7}{9}$ x = 1

Half the x- term coefficient, square it and add this value to both sides.

x-term coefficient = -$\frac{7}{9}$

Half the x-term coefficient = -$\frac{7}{18}$

After Squaring = $\frac{49}{324}$

Add this value to both sides

$x^{2}$ - $\frac{7}{9}$x + $\frac{49}{324}$ = 1 + $\frac{49}{324}$

Simplifying the above

$x^{2}$ - $\frac{7}{9}$x + $\frac{49}{324}$ = $\frac{373}{324}$

The left side of the expression should be converted to perfect square and by taking square root on both sides

(x-$\frac{7}{18}$$)^{2}$ = $\frac{373}{324}$

x-$\frac{7}{18}$ = $\pm\sqrt{\frac{373}{324}}$

Solve for x:

x = $\frac{7}{18}$$\pm\sqrt{\frac{373}{324}}$

$x_{1}$ = $\frac{7}{18}$ + $\frac{1}{18}\sqrt{373}$

$x_{2}$ = $\frac{7}{18}$ - $\frac{1}{18}\sqrt{373}$