Solve by (a) Completing the square (b) Using the quadratic formula x^2+17 x-8=0

Name: Problem 34, Chapter 9: Algebra Form and Function
Uploaded: 2022-04-06T20:23:07-08:00
Duration: 2 min
Channel: Alison Rodriguez
Description: Solve by (a) Completing the square (b) Using the quadratic formula x^2+17 x-8=0

step 1 To begin the complete in the square process for part A, we're going to move the 8x over to the r

Solve by (a) Completing the square (b) Using the quadratic...

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two, generally expressed in the form ax² + bx + c = 0. These equations are fundamental in algebra and have applications in various fields, including physics and engineering. Understanding their structure helps in selecting appropriate methods—such as factoring, completing the square, or using the quadratic formula—to find their roots.

Completing the Square

Completing the square is a method used to transform a quadratic equation into a perfect square trinomial. This technique involves manipulating the equation so that one side forms an expression that can be written as (x + d)², making it easier to solve for x by taking the square root of both sides. It is a useful method not only for solving equations but also for understanding the derivation of the quadratic formula and analyzing the properties of quadratic functions.

Quadratic Formula

The quadratic formula is a universal method for solving quadratic equations of the form ax² + bx + c = 0. It is derived from the process of completing the square and provides a straightforward calculation for the roots: x = (-b ± ?(b² - 4ac)) / (2a). This formula is especially useful when the quadratic does not factor easily or when a general solution is required.

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