Question

Solve the equation by factoring. $$ x^{2}+3 x=54 $$

   Solve the equation by factoring.
$$
x^{2}+3 x=54
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 10, Problem 29

Instant Answer

Solved by Expert Cory Kuzinski

04/20/2020

Step 1

We can do this by subtracting 54 from both sides of the equation: $$x^2 + 3x - 54 = 0$$ Show more…

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Solve the equation by factoring. $$ x^{2}+3 x=54 $$

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Key Concepts

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 with a ? 0. Quadratic equations form the basis for many algebraic problem-solving techniques and have characteristic parabolic graphs.

Standard Form

Rewriting an equation in standard form involves arranging it so that all terms are on one side of the equation, set equal to zero. This conversion is a crucial step when using methods like factoring or the quadratic formula to solve the equation.

Factoring

Factoring is a method of breaking down a polynomial into a product of simpler polynomials, typically binomials in the case of quadratics. This technique simplifies problem solving by reducing a complex equation into parts that can be solved more easily.

Zero Product Property

The zero product property states that if a product of factors equals zero, then at least one of the factors must be zero. This principle allows one to solve factored equations by setting each individual factor equal to zero and solving the resulting equations.

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