Question

Solve using any method. $$v^{2}-8 v=-20$$

   Solve using any method.
$$v^{2}-8 v=-20$$

Precalculus

Cynthia Young 2nd Edition

Chapter 0, Problem 60

Instant Answer

Solved by Expert Ernest Castorena

07/01/2020

Step 1

Step 1: First, we rewrite the equation as follows: $$v^{2}-8 v+20=0$$ Show more…

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically written in the standard form ax² + bx + c = 0. Understanding quadratic equations is essential because they appear frequently in various areas of mathematics and science, and they often have two solutions which can be real or complex.

Standard Form Transformation

Rewriting an equation into its standard form involves moving all terms to one side so that the equation is set to zero. This step is crucial as it prepares the equation for application of various solution methods, like factoring, completing the square, or using the quadratic formula.

Factoring

Factoring is a technique to solve quadratic equations by expressing the quadratic as a product of two simpler binomial expressions. When the quadratic factors neatly, setting each binomial factor equal to zero yields the solutions of the equation.

Completing the Square

Completing the square transforms a quadratic expression into a perfect square trinomial plus a constant. This method not only aids in solving quadratic equations but also provides insights into the graph of the quadratic function by revealing its vertex form.

Quadratic Formula

The quadratic formula is a comprehensive method for solving any quadratic equation, regardless of whether it factors neatly or not. It is given by x = (-b ± ?(b² - 4ac))/(2a), and it is derived from the process of completing the square. This formula is particularly useful for determining the nature of the roots based on the discriminant.

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