Question

question

use the quadratic formula to solve. express your answer in simplest form.

\\5c^2 + 12c + 4 = 0\\

Explanation:

Identify coefficients

$$ a = 5, \quad b = 12, \quad c = 4 $$

Calculate discriminant

$$ D = b^2 - 4ac = 12^2 - 4(5)(4) = 144 - 80 = 64 $$

Apply quadratic formula

$$ c = \frac{-b \pm \sqrt{D}}{2a} = \frac{-12 \pm \sqrt{64}}{2(5)} = \frac{-12 \pm 8}{10} $$

$$ c_1 = \frac{-12 + 8}{10} = -\frac{4}{10} = -\frac{2}{5} $$

$$ c_2 = \frac{-12 - 8}{10} = -\frac{20}{10} = -2 $$

Answer:

Use the quadratic formula to solve. Express your answer in simplest form.
\(5c^2 + 12c + 4 = 0\)

\(c =\) <blank>\(-\frac{2}{5}, -2\)</blank>