Question

Solve the quadratic equation by factoring. $$x^{2}-25=0$$

   Solve the quadratic equation by factoring.
$$x^{2}-25=0$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 2, Problem 9

Instant Answer

Solved by Expert Joseph Towne

05/08/2020

Step 1

We can see that this equation is in the form of a difference of squares, $a^{2}-b^{2}$, where $a=x$ and $b=5$. Show more…

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Solve the quadratic equation by factoring. $$x^{2}-25=0$$

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Key Concepts

Quadratic Equation

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants with a ? 0. Solving quadratic equations involves finding the values of x that satisfy the equation and can be done by various methods including factoring, completing the square, or using the quadratic formula.

Difference of Squares

The difference of squares is a specific factoring pattern that occurs when an expression is of the form a² - b², which can be factored into (a + b)(a - b). Recognizing this pattern simplifies the factorization process for certain quadratic equations.

Zero-Product Property

The zero-product property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property is fundamental in solving factored quadratic equations, as it allows one to set each factor equal to zero and solve for the variable.

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