Explanation Given information: The provided equation is 27 − 3 x = x − 3 . Formula used: Principle of squaring states that if two numbers, a and b are equal, their squares are equal as well. Mathematically, If a = b then a 2 = b 2 Follow the steps to solve the problem: Step1: Isolate one of the radical terms on one side of the equation. Step2: Apply the principle of squaring. Step3: Perform steps 1 and 2 again if there remains a radical expression in the equation. Step4: Solve the equation. Step5: Verify the solutions obtained. The following expansion formula is used: ( a − b ) 2 = a 2 − 2 a b + b 2 In such type of questions, factorize the given polynomial and then apply the principle of zeroes. Principle of zeroes states that if the product of two or more expressions is 0 then either one or two or all of them are 0 . Calculation: Consider the equation, 27 − 3 x = x − 3 Apply the principle of squares and expand using the quadratic expansion, ( 27 − 3 x ) 2 = ( x − 3 ) 2 27 − 3 x = x 2 − 6 x + 9 Subtract 27 − 3 x from both the sides, 27 − 3 x − ( 27 − 3 x ) = x 2 − 6 x + 9 − ( 27 − 3 x ) 0 = x 2 − 3 x − 18 x 2 − 3 x − 18 = 0 Factorize the polynomial by splitting the middle term, x 2 + 3 x − 6

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 14.5, Problem 26ES

To determine

To calculate: The value of x for the equation 27−3x=x−3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 25ES

Chapter 14.5, Problem 27ES

Students have asked these similar questions

- Suppose that you have the differential equation: dy = (y - 2) (y+3) dx a. What are the equilibrium solutions for the differential equation? b. Where is the differential equation increasing or decreasing? Show how you know. Showing them on the drawing is not enough. c. Where are the changes in concavity for the differential equation? Show how you know. Showing them on the drawing is not enough. d. Consider the slope field for the differential equation. Draw solution curves given the following initial conditions: i. y(0) = -5 ii. y(0) = -1 iii. y(0) = 2

5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1

4. Given the following information determine the appropriate trial solution to find yp. Do not solve the differential equation. Do not find the constants. a) (D-4)2(D+ 2)y = 4e-2x b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3x

Chapter 14 Solutions

DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<

Ch. 14.1 - Prob. 1SR Ch. 14.1 - Prob. 2SR Ch. 14.1 - Prob. 1DE Ch. 14.1 - Prob. 2DE Ch. 14.1 - Prob. 3DE Ch. 14.1 - Prob. 4DE Ch. 14.1 - Prob. 5DE Ch. 14.1 - Prob. 6DE Ch. 14.1 - Prob. 7DE Ch. 14.1 - Prob. 8DE

Knowledge Booster

Learn more about

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

The value of x for the equation 27 − 3 x = x − 3 .

Solution Summary: The author explains how to calculate the value of x for the equation sqrt27-3x=x-3.

Concept explainers

Videos

To calculate: The value of x for the equation 27−3x=x−3.

Want to see the full answer?

Chapter 14 Solutions