Question

solve equation by using the quadratic formula. list the solutions, separated by commas.

\\4r^2 - 3r - 2 = 0\\

\\(r =\\)

Explanation:

Identify coefficients of the quadratic equation

$$ a = 4, \quad b = -3, \quad c = -2 $$

Apply the quadratic formula

$$ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ r = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(4)(-2)}}{2(4)} $$

Simplify the expression

$$ r = \frac{3 \pm \sqrt{9 + 32}}{8} $$

$$ r = \frac{3 \pm \sqrt{41}}{8} $$

Answer:

Solve equation by using the quadratic formula. List the solutions, separated by commas.
\(4r^2 - 3r - 2 = 0\)
\(r =\) <blank>\(\frac{3+\sqrt{41}}{8},\frac{3-\sqrt{41}}{8}\)</blank>