Question

2x2 + 5 = 6x Solve using the quadratic formula with the answer as a+bi form

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} 2x^2+5=6x \\ 2x^2-6x+5=0 \\ a=2,b=-6,c=5 \end{gathered}`

We proceed to use the quadratic formula, we have:

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ a=2,b=-6,c=5 \\ x=\frac{-(-6)\pm\sqrt[]{-6^2-4(2\cdot5)}}{2(2)} \\ x=\frac{6\pm\sqrt[]{36-40}}{4}=x=\frac{6\pm\sqrt[]{-4}}{4} \\ \sqrt[]{-4}=2i \\ x=\frac{6\pm\sqrt[]{-4}}{4}\Rightarrow(6\pm2i)/(4) \\ x=(6)/(4)+(2i)/(4),(6)/(4)-(2i)/(4) \\ x_1=1.5+0.5i \\ x_2=1.5-0.5i \end{gathered}`