Question

1. \\(4x^2 - x = 14\\)

\\(a = \underline{\quad\quad}\quad b = \underline{\quad\quad}\quad c = \underline{\quad\quad}\\)
\\(x = \frac{- (\quad) \pm \sqrt{(\quad)^2 - 4(\quad)(\quad)}}{2(\quad)}\\)

Explanation:

Step1: Rewrite to standard quadratic form

Rearrange $4x^2 - x = 14$ to $4x^2 - x - 14 = 0$. The standard quadratic form is $ax^2 + bx + c = 0$.

Step2: Identify a, b, c values

Compare $4x^2 - x - 14 = 0$ to $ax^2 + bx + c = 0$:
$a = 4$, $b = -1$, $c = -14$

Step3: Substitute into quadratic formula

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Substitute the identified values.

Answer:

$a = 4$, $b = -1$, $c = -14$
$x = \frac{-(-1)\pm\sqrt{(-1)^2-4(4)(-14)}}{2(4)}$