Video narration
Let’s solve the quadratic equation x^2 + 5x + 3 = 0. Since it doesn’t factor nicely, we’ll use the quadratic formula: for ax^2 + bx + c = 0, x equals negative b plus or minus the square root of b squared minus 4ac, all over 2a. Here, a = 1, b = 5, and c = 3. Substitute them in: x = (−5 ± √(5^2 − 4·1·3)) / (2·1). Now simplify inside the square root: 5^2 is 25, and 4·1·3 is 12, so the discriminant is 25 − 12 = 13. That gives x = (−5 ± √13) / 2. So the two roots are x = (−5 + √13)/2 and x = (−5 − √13)/2.