Skip to main content
Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 55
Chapter 2, Problem 55

Solve each equation in Exercises 47–64 by completing the square. x2−5x+6=0x^2 - 5x + 6 = 0

Verified step by step guidance
1
Start with the given quadratic equation: \(x^2 - 5x + 6 = 0\).
Move the constant term to the other side to isolate the quadratic and linear terms: \(x^2 - 5x = -6\).
To complete the square, take half of the coefficient of \(x\), which is \(-5\), divide by 2 to get \(-\frac{5}{2}\), then square it to get \(\left(-\frac{5}{2}\right)^2 = \frac{25}{4}\).
Add \(\frac{25}{4}\) to both sides of the equation to maintain equality: \(x^2 - 5x + \frac{25}{4} = -6 + \frac{25}{4}\).
Rewrite the left side as a perfect square trinomial: \(\left(x - \frac{5}{2}\right)^2 = -6 + \frac{25}{4}\). From here, you can simplify the right side and solve for \(x\) by taking the square root of both sides.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

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

Completing the Square

Completing the square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. This involves adding and subtracting a specific value to create a binomial squared, making it easier to solve for the variable.
Recommended video:
06:24
Solving Quadratic Equations by Completing the Square

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0. Understanding its structure is essential for applying methods like factoring, completing the square, or using the quadratic formula to find the roots.
Recommended video:
05:35
Introduction to Quadratic Equations

Solving Equations Using Square Roots

Once a quadratic equation is written as a perfect square equal to a constant, you can solve it by taking the square root of both sides. This step introduces both positive and negative roots, which are critical for finding all solutions.
Recommended video:
06:12
Solving Quadratic Equations by the Square Root Property
Related Practice
Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 2) + 2/(x - 2) = 8/(x + 2)(x - 2)

1168
views
Textbook Question

Write each power of i as i, - 1, - i, or 1.

i44

892
views
Textbook Question

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)2 - 4(x - 5) - 21 = 0

639
views
Textbook Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R1 + 1/R2 for R1

617
views
Textbook Question

In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

768
views
Textbook Question

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

903
views