Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 18

Chapter 2, Problem 18

Solve each equation in Exercises 15–34 by the square root property. 3x² - 1 = 47

Verified step by step guidance

Start by isolating the quadratic term. Add 1 to both sides of the equation to eliminate the constant term on the left-hand side:

3x^2 = 47 + 1

Simplify the right-hand side to combine the constants:

3x^2 = 48

Divide both sides of the equation by 3 to isolate

x^2

x^2 = \(\frac{48}{3}\)

Simplify the fraction on the right-hand side:

x^2 = 16

Apply the square root property to solve for

x

. Remember to include both the positive and negative roots:

x = \(\pm\) \(\sqrt{16}\)

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Square Root Property

The square root property states that if an equation is in the form of x^2 = k, then the solutions for x can be found by taking the square root of both sides, resulting in x = ±√k. This property is essential for solving quadratic equations where the variable is squared.

Rearranging Equations

Rearranging equations involves manipulating the equation to isolate the variable of interest. In the context of the given equation, this means moving all terms to one side to set the equation to zero or isolating the squared term to apply the square root property effectively.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. Understanding the standard form of quadratic equations is crucial for applying various solving techniques, including the square root property, factoring, and the quadratic formula.

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