Question

Solve using the zero-factor property. $$ x^{2}-400=0 $$

   Solve using the zero-factor property.
$$
x^{2}-400=0
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 11, Problem 16

Instant Answer

Solved by Expert Nick Johnson

02/10/2022

Step 1

The equation is a difference of squares, which can be factored as $(a+b)(a-b)$. Here, $a=x$ and $b=20$. So, we can write the equation as: $$ (x+20)(x-20)=0 $$ Show more…

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Solve using the zero-factor property. $$ x^{2}-400=0 $$

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Key Concepts

Quadratic Equations

Quadratic Equations are polynomial equations of degree two and can be solved by various methods including factoring, completing the square, and the quadratic formula. Understanding these equations and their solutions forms a fundamental part of algebra.

Difference of Squares

The Difference of Squares is a factoring technique used when an expression takes the form a² - b². It can be rewritten as (a + b)(a - b), which simplifies the process of solving the equation by breaking it into easier factors.

Zero-Factor Property

The Zero-Factor Property states that if the product of two or more factors equals zero, then at least one of the factors must equal zero. This idea is crucial in solving equations where the expression can be factored, as it allows the equation to be broken down into simpler linear pieces.

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