Question

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

Explanation:

Step1: Simplify the numerator's first term

$-(-1) = 1$

Step2: Calculate the discriminant

$\sqrt{(-1)^2 - 4(4)(-14)} = \sqrt{1 + 224} = \sqrt{225} = 15$

Step3: Simplify the denominator

$2(4) = 8$

Step4: Split into two solutions

First solution: $x = \frac{1 + 15}{8}$; Second solution: $x = \frac{1 - 15}{8}$

Step5: Compute each solution

$\frac{1 + 15}{8} = \frac{16}{8} = 2$; $\frac{1 - 15}{8} = \frac{-14}{8} = -\frac{7}{4}$

Answer:

$x = 2$ and $x = -\frac{7}{4}$