Solve x^2+2 x-10=0 by completing the square.

Name: Problem 108, Chapter 9: Intermediate Algebra for College Students
Uploaded: 2022-02-10T06:16:44-08:00
Duration: 35 s
Channel: Victor Salazar
Description: Solve x^2+2 x-10=0 by completing the square.

Key Concepts

Completing the Square

Completing the square is a method used to convert a quadratic equation from its standard form into a perfect square trinomial plus or minus a constant. This technique involves creating a squared binomial, which simplifies the process of solving the equation by making it possible to apply the square root property. It is a valuable tool not only for solving equations but also for analyzing the properties of quadratic functions, such as finding the vertex of a parabola.

Square Root Property

Once a quadratic equation has been rewritten in the form (x + d)² = e through completing the square, the square root property is applied to solve for x. This property states that if (x + d)² = e, then x + d is equal to the positive or negative square root of e. This step is essential in isolating the variable and arriving at the solution of the quadratic equation.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants with a ? 0. This form allows for the analysis and solution of the equation through various techniques, making it a fundamental concept in algebra and essential for understanding parabolic curves in geometry.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation, ax² + bx + c = 0, provides a starting point for many solution techniques, including completing the square and using the quadratic formula. Having the equation in standard form makes it easier to identify the coefficients and structure of the equation, which is critical for accurate manipulation and solving.

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