Question

Using the quadratic formula, solve 0 = 2x² - 14x + 9

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \text{$ \sf 2x^2 - 14x + 9 = 0$}`

`\Large \text{$ \sf a = 2$}`

`\Large \text{$ \sf b = -14$}`

`\Large \text{$ \sf c = 9$}`

`\Large \text{$ \sf \Delta = b^2 - 4.a.c$}`

`\Large \text{$ \sf \Delta = (-14)^2 - 4.2.9$}`

`\Large \text{$ \sf \Delta = 196 - 72$}`

`\Large \text{$ \sf \Delta = 124$}`

`\Large \text{$ \sf x = (-b \pm √(\Delta))/(2a) = (14 \pm √(124))/(4) \rightarrow \begin{cases}\sf{x' = (7 + √(31))/(2)}\\\\\sf{x'' = (7 - √(31))/(2)}\end{cases}$}`

`\Large \text{$ \sf S = \left\{ (7 + √(31))/(2),\: (7 - √(31))/(2)\right\}$}`