Solve. x 2+2 x-√(3)+5=7

Name: Problem 68, Chapter 8: Elementary Algebra
Uploaded: 2022-02-03T19:45:09-08:00
Duration: 31 s
Channel: James Kiss
Description: Solve. x 2+2 x-√(3)+5=7

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation usually written in the form ax² + bx + c = 0. It forms the basis for many algebraic methods and appears in various fields of mathematics and science, requiring techniques like factoring, completing the square, or applying the quadratic formula to find its solutions.

Standard Form

Rearranging an equation to its standard form means writing it as ax² + bx + c = 0. This restructuring is crucial because it allows for the consistent identification of coefficients, enabling the use of standard solving techniques, including the quadratic formula or factoring.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a general method used to solve any quadratic equation. It is derived by completing the square on the general quadratic equation and provides the solutions in terms of the coefficients a, b, and c.

Discriminant

The discriminant, given by b² - 4ac, is a component of the quadratic formula that determines the nature of the roots of the quadratic equation. It helps in identifying whether the solutions are real or complex and whether they are distinct or repeated.

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