Solve each equation using the quadratic formula. Simplify solutions, if possible. 9 x^2+x=-2

Name: Problem 12, Chapter 8: Introductory and Intermediate Algebra for College Students
Uploaded: 2020-09-03T18:53:15-08:00
Duration: 2 min 1 s
Channel: Ankit Gupta
Description: Solve each equation using the quadratic formula. Simplify solutions, if possible. 9 x^2+x=-2

step 1 According to the question, we have to solve a quadratic equation 9xx squared plus x equals minus

Solve each equation using the quadratic formula. Simplify...

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Key Concepts

Discriminant

The discriminant in a quadratic equation is the expression b² - 4ac, found under the square root in the quadratic formula. It determines the nature of the roots: if it is positive, there are two distinct real solutions; if zero, there is exactly one real solution (a repeated root); and if negative, the solutions are complex conjugates.

Quadratic Formula

The quadratic formula, given by x = (-b ± ?(b² - 4ac)) / (2a), is a universal method for finding the solutions to any quadratic equation. It is derived by completing the square on the standard form of the equation and provides insight into the nature of the solutions through its structure.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. This type of equation can have two real solutions, one real solution, or two complex solutions depending on the values of the coefficients.

Standard Form

Converting an equation to standard form is the process of rewriting it so that all terms are on one side of the equal sign with zero on the other side, arranging the terms in descending order of power. This is a necessary step for applying most solution techniques, including the quadratic formula.

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