Question

Solve the equation by using the Quadratic Formula.

2⁢𝑥^2+2⁢𝑥+3=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 = 2, b = 2, c = 3.

Discriminant: b^2 - 4ac = 4 - 24 = -20.

x = [-2 ± sqrt(-20)]/(4) = [-2 ± i·2√5]/4 = (-1 ± i√5)/2.

So the solutions are (-1/2) ± (√5/2) i.