Question

Solve the equation by using the Quadratic Formula.

4⁢𝑥^2+2⁢𝑥+9=0

Simplify your solutions. If the solutions are real rational numbers, list from least to greatest separated by a comma. If the solutions are not real numbers, write your answer in the form a ± bi. If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.

Answer 1

Use the quadratic formula x = [-b ± sqrt(b^2 − 4ac)]/(2a) with a = 4, b = 2, c = 9:

Discriminant: b^2 − 4ac = 4 − 144 = −140 = −(140) = −4·35.

x = [−2 ± sqrt(−140)]/(8) = [−2 ± 2i√35]/8 = [−1 ± i√35]/4.

So the solutions are: −1/4 ± (√35/4) i.