   Chapter 0.5, Problem 23E

Chapter
Section
Textbook Problem

By any method, determine all possible real solutions of each equation in Exercises 13–30. Check your answers by substitution. x 2 − x = 1

To determine

To calculate: The all real solutions in the quadratic equation x2x=1.

Explanation

Given Information:

The provided quadratic equation is x2x=1.

Formula used:

The value of x in the equation ax2+bx+c=0 can be given by the quadratic formula,

x=b±b24ac2a where a,b and c are real numbers with a0.

Calculation:

Consider the quadratic equation x2x=1.

Subtract 1 from both sides in the above equation,

x2x1=11x2x1=0

Compare the above equation with the equation ax2+bx+c=0,

a=1, b=1 and c=1

Put the values of a,b,c in the quadratic formula x=b±b24ac2a.

x=(1)±(1)241(1)21=1±1+42=1±52

Further simplify,

x=1+52 Or 152

Check:

For x=152

Substitute the value of x=152 in x2x=1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate the expression sin Exercises 116. (23)2

Finite Mathematics and Applied Calculus (MindTap Course List)

What is the slope of a nonvertical line? What can you say about the slope of a vertical line?

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the integrals in Problems 1-32.

Mathematical Applications for the Management, Life, and Social Sciences

Solve for if 0360. cos2cos=0

Trigonometry (MindTap Course List)

Let f(x)={2x2forx13forx1. Which limit does not exist? a) limx3f(x) b) limx1+f(x) c) limx1f(x) d) limx1f(x)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 