Question

the solutions to the equation $5x^2 - 2x + 13 = 9$ are

1. $\frac{1}{5} pm \frac{sqrt{21}}{5}$
2. $\frac{1}{5} pm \frac{sqrt{19}}{5}i$
3. $\frac{1}{5} pm \frac{sqrt{66}}{5}i$
4. $\frac{1}{5} pm \frac{sqrt{66}}{5}$

Explanation:

Step1: Rewrite equation in standard form

$5x^2 - 2x + 4 = 0$

Step2: Identify coefficients

$a=5, b=-2, c=4$

Step3: Calculate discriminant

$\Delta = (-2)^2 - 4(5)(4) = 4 - 80 = -76$

Step4: Apply quadratic formula

$x = \frac{-(-2)\pm\sqrt{-76}}{2(5)} = \frac{2\pm2\sqrt{19}i}{10} = \frac{1}{5}\pm\frac{\sqrt{19}}{5}i$

Answer:

1. $\frac{1}{5}\pm\frac{\sqrt{19}}{5}i$