Skip to main content
Ch. 1 - Equations and Inequalities
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 1 - Equations and InequalitiesProblem 91
Chapter 2, Problem 91

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | x2 + 5x + 5 | = 1

Verified step by step guidance
1
Recognize that the equation involves an absolute value: \(|x^2 + 5x + 5| = 1\). The absolute value of an expression equals 1 means the expression inside the absolute value can be either 1 or -1.
Set up two separate equations based on the definition of absolute value: 1) \(x^2 + 5x + 5 = 1\) 2) \(x^2 + 5x + 5 = -1\)
Solve the first quadratic equation \(x^2 + 5x + 5 = 1\) by moving all terms to one side to set it equal to zero: \(x^2 + 5x + 5 - 1 = 0\) which simplifies to \(x^2 + 5x + 4 = 0\)
Solve the second quadratic equation \(x^2 + 5x + 5 = -1\) similarly by moving all terms to one side: \(x^2 + 5x + 5 + 1 = 0\) which simplifies to \(x^2 + 5x + 6 = 0\)
Use factoring, completing the square, or the quadratic formula to find the roots of each quadratic equation. The solutions to these equations will be the solutions to the original absolute value equation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

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

Absolute Value Equations

An absolute value equation involves the expression |A| = B, where B ≥ 0. It means that the quantity inside the absolute value, A, can be either B or -B. To solve, split the equation into two cases: A = B and A = -B, then solve each separately.
Recommended video:
06:00
Categorizing Linear Equations

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solutions can be found by factoring, completing the square, or using the quadratic formula. Understanding how to solve quadratics is essential when the absolute value expression contains a quadratic.
Recommended video:
05:35
Introduction to Quadratic Equations

Properties of Absolute Value Inequalities and Equations

Properties of absolute value help simplify and solve equations or inequalities involving absolute values. For example, |A| = B implies A = B or A = -B, while |A| ≤ B implies -B ≤ A ≤ B. Recognizing these properties allows for correct splitting and solving of the given equation.
Recommended video:
06:12
Solving Quadratic Equations by the Square Root Property
Related Practice
Textbook Question

Solve each equation. (2x-1)2/3+2(2x-1)1/3-3=0

354
views
Textbook Question

Solve each equation. (x-1)2/3+(x-1)1/3 -12 = 0

411
views
Textbook Question

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

8x2−72=08x^2 - 72 = 0

893
views
Textbook Question

Simplify each power of i. i29

867
views
Textbook Question

Solve each problem. A baseball is hit so that its height, s, in feet after t seconds is s=-16t2+44t+4. For what time period is the ball at least 32 ft above the ground?

549
views
Textbook Question

Simplify each power of i. i26

922
views