Question

use the quadratic formula to solve the equation.\
\\(-8 = 4x^2 + x\\)\
\\(x = \square\\)\
(use integers or fractions for any numbers in the expression. express c

Explanation:

Step1: Rearrange to standard form

$4x^2 + x + 8 = 0$

Step2: Identify a, b, c

For $ax^2+bx+c=0$, $a=4$, $b=1$, $c=8$

Step3: Substitute into quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{-1\pm\sqrt{1^2-4\times4\times8}}{2\times4}$

Step4: Calculate discriminant

$\sqrt{1-128}=\sqrt{-127}=i\sqrt{127}$

Step5: Simplify the expression

$x=\frac{-1\pm i\sqrt{127}}{8}$

Answer:

$x=\frac{-1+i\sqrt{127}}{8}$ and $x=\frac{-1-i\sqrt{127}}{8}$