Solve each equation using completing the square. x2 - 2x - 2 = 0

Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 41

Chapter 2, Problem 41

Solve each equation using completing the square. x² - 2x - 2 = 0

Verified step by step guidance

Start with the given quadratic equation: \(x^2 - 2x - 2 = 0\).

Move the constant term to the other side to isolate the quadratic and linear terms: \(x^2 - 2x = 2\).

To complete the square, take half of the coefficient of \(x\), which is \(-2\), divide by 2 to get \(-1\), then square it to get \((-1)^2 = 1\).

Add this square to both sides of the equation to maintain equality: \(x^2 - 2x + 1 = 2 + 1\).

Rewrite the left side as a perfect square trinomial: \((x - 1)^2 = 3\). From here, you can proceed by taking the square root of both sides to solve for \(x\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

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.

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 completing the square, factoring, or using the quadratic formula to find the roots.

Isolating the Variable

Isolating the variable involves rearranging the equation so that the variable term stands alone on one side. This step is crucial before completing the square, as it simplifies the process of forming a perfect square trinomial and solving the equation.

Recommended video:

Guided course

05:28

Equations with Two Variables

Related Practice

Textbook Question

Solve each equation. -2x² +11x = -21

Textbook Question

Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9

Textbook Question

Length of a Walkway A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway.

Textbook Question

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

views

Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation. x²-7x+10<0