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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 4
Chapter 2, Problem 4

Match the equation in Column I with its solution(s) in Column II. x2 - 5 = 0
Matching exercise with equations involving squares and their corresponding solutions including real and imaginary numbers.

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1
Start with the given equation: \(x^2 - 5 = 0\).
Isolate the squared term by adding 5 to both sides: \(x^2 = 5\).
To solve for \(x\), take the square root of both sides: \(x = \pm \sqrt{5}\).
Remember that taking the square root introduces both positive and negative solutions, so the solutions are \(x = \sqrt{5}\) and \(x = -\sqrt{5}\).
Match these solutions with the corresponding option in Column II that lists \(x = \pm \sqrt{5}\).

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Key Concepts

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

Solving Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solving it involves finding values of x that satisfy the equation, often by factoring, completing the square, or using the quadratic formula.
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Isolating the Variable

Isolating the variable means manipulating the equation to get the variable alone on one side. For example, in x² - 5 = 0, adding 5 to both sides isolates x², making it easier to solve for x by taking square roots.
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Equations with Two Variables

Square Root Property

The square root property states that if x² = k, then x = ±√k. This means when solving equations like x² = 5, the solutions are both the positive and negative square roots of 5, reflecting two possible values for x.
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Imaginary Roots with the Square Root Property
Related Practice
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Match the inequality in each exercise in Column I with its equivalent interval notation in Column II . x≥-6

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Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

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Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. x2≥0

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Answer each question. Sides of a Right TriangleTo solve for the lengths of the right triangle sides, which equation is correct?

A. x^2=(2x-2)^2+(x+4)^2 B. x^2+(x+4)^2=(2x-2)^2 C. x^2=(2x-2)^2-(x+4)^2 D. x^2+(2x-2)^2=(x+4)^2

Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > -7

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