Question

Solve –2x2 +3x – 9 = 0

Answer 1

\[\begin{array}{l} \text{Solve the quadratic equation by completing the square}\text{}~~\text{Divide both sides by }-2: \\ x^2-\frac{3 x}{2}+\frac{9}{2}=0 \\ \text{Subtract }\frac{9}{2}\text{ from both sides:} \\ x^2-\frac{3 x}{2}=-\frac{9}{2} \\ \text{Add }\frac{9}{16}\text{ to both sides:} \\ x^2-\frac{3 x}{2}+\frac{9}{16}=-\frac{63}{16} \\ \text{Factor the \left hand side:} \\ \left(x-\frac{3}{4}\right)^2=-\frac{63}{16} \\\end{array}\]
solve by square rooting it, but you'll get complex number

Answer 2

x=13/4