Explanation Given Information: The equation is 0.1 x 2 − 0.2 x − 0.1 = 0 . Formula used: The standard form of the quadratic equation is, a x 2 + b x + n = 0 Here, a , b , and n are the constants or number. Also, if the above quadratic equation is a perfect square. Then, n = [ 1 2 ( b ) ] 2 Here, b is the coefficient of x . Calculation: Consider the provided the equation, 0.1 x 2 − 0.2 x − 0.1 = 0 Add 0.1 on the both sides. 0.1 x 2 − 0.2 x − 0.1 + 0.1 = 0 + 0.1 0.1 x 2 − 0.2 x = 0.1 Dividing by 0.1 both sides. x 2 − 2 x = 1 On comparing x 2 − 2 x + N with the standard form of the quadratic equation a x 2 + b x + n , x 2 − 2 x + N is a complete square, for N = ( 1 2 b ) 2 . Here, b is the coefficient of x . Substitute − 2 for b . N = ( 1 2 ( − 2 ) ) 2 = ( − 1 ) 2 = 1 Thus, the value of N to complete the square for the equation x 2 − 2 x = 1 is 1 . Add 1 on the both sides of the equation, x 2 − 2 x = 1 . Hence, x 2 − 2 x + 1 = 1 + 1 x 2 − 2 x + 1 = 2 Factorize the equation for the calculating the complete square form of the equation. x 2 − x − x + 1 = 2 x ( x − 1 ) − 1 ( x − 1 ) = 2 ( x − 1 ) ( x − 1 ) = 2 ( x − 1 ) 2 = 2 Apply the square root property to simplify the equation

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 11.2, Problem 49E

To determine

To calculate: The solution of the equation 0.1x2−0.2x−0.1=0 by completing the square.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.2, Problem 48E

Chapter 11.2, Problem 50E

Students have asked these similar questions

The height of a sunflower plant can be determined by the time t in weeks after the seed has germinated. Write a model to represent the height h if the height is given by the product of 8 and the square root of t.

solve for w. 9- the square root of w = the square root of w-27

refer to image

Chapter 11 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 11.1 - Concept Check Answer each question. 1. Which of...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 6E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 8E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The solution of the equation 0.1 x 2 − 0.2 x − 0.1 = 0 by completing the square.

Solution Summary: The author calculates the solution of the equation 0.1x2-0.2x-0.1=0 by completing the square.

Concept explainers

Videos

To calculate: The solution of the equation 0.1x2−0.2x−0.1=0 by completing the square.

Want to see the full answer?

Chapter 11 Solutions