   Chapter 0.5, Problem 22E

Chapter
Section
Textbook Problem

By any method, determine all possible real solutions of each equation in Exercises 13–30. Check your answers by substitution. − 1 2 x 2 − 1 2 x + 1 = 0

To determine

To calculate: The all real solutions in the quadratic equation 12x212x+1=0.

Explanation

Given Information:

The provided quadratic equation is 12x212x+1=0.

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 12x212x+1=0.

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

a=12, b=12 and c=1

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

x=(12)±(12)24(12)12(12)=12±14+21=12±941=12±321

Further simplify,

x=12±321

Therefore,

=12+321=1+321=421=2

Or

x=12321=1321=221=1

Check:

For x=1

Substitute the value of x=1 in 12x212x+1=0

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