Problems 134–137 are based on material learned earlier in...

Problems 134–137 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
$$
\text { Solve: } 5 x^{2}+2=5-14 x
$$

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Key Concepts

Quadratic Formula

The quadratic formula, given by x = (–b ± ?(b² – 4ac))/(2a), is a universal tool for solving any quadratic equation. It is particularly useful when the equation does not factor neatly, offering a direct method to find the roots using the coefficients from the standard form.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations, combining like terms, and simplifying expressions to transform complex equations into a more workable form. Mastery of these skills is essential for solving equations, as it allows for the systematic conversion of problems into standard forms suited for established solution methods.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically expressed in the form ax² + bx + c = 0. Understanding quadratic equations is fundamental in algebra as they model parabolic behavior and appear in various real-life applications including physics and economics.

Standard Form of a Quadratic Equation

Rewriting a quadratic equation in the standard form, ax² + bx + c = 0, is crucial for systematically applying solution techniques. This form organizes the terms in descending powers of the variable, making it easier to identify coefficients and apply methods like factoring or the quadratic formula.

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