The speaker explains how to use the quadratic formula (also known as the "Basque formula") to solve quadratic equations. They start with a quadratic equation in the form of ax^2 + bx + c = 0 and explain how to plug in the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
The speaker then works through an example problem with the values a = 2, b = 9, and c = 7. They plug these values into the quadratic formula and simplify the equation to find the two solutions for x.
The speaker explains the rules for working with signs and numbers, and demonstrates how to solve the equation step by step. They also discuss how to find the square root of a number and how to simplify expressions.
In the end, the speaker finds the two solutions for x: x1 = 4/4 = 1 and x2 = -14/4 = -3.5. They explain that these solutions represent the x-intercepts of a parabola and that the quadratic formula can be used to find these intercepts.
Here are the key facts extracted from the text:
1. The Basque formula, also known as the quadratic formula, is used to calculate the value of x.
2. The Basque formula is x = (-b ± √(b² - 4ac)) / 2a.
3. The quadratic equation is ax² + bx + c = 0.
4. To use the Basque formula, you need to know the values of a, b, and c.
5. In this example, a = 2, b = 9, and c = 7.
6. The first step is to calculate b² - 4ac.
7. 9² = 81.
8. 4 times 2 times 7 = 56.
9. 81 - 56 = 25.
10. The square root of 25 is 5.
11. There are two possible values for x: x = (-9 + 5) / 4 and x = (-9 - 5) / 4.
12. x1 = (-9 + 5) / 4 = -4 / 4 = -1.
13. x2 = (-9 - 5) / 4 = -14 / 4 = -3.5.
14. The values of x1 and x2 are the real roots of the quadratic equation.
15. The Basque formula is used to calculate the real or imaginary roots of a quadratic equation.