   Chapter A.4, Problem 34E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 33 to 36, solve each incomplete quadratic equation. 16 x 2 - 9 = 0

To determine

To solve:

The incomplete quadratic equation

16x2-9=0

Explanation

Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.

Calculation:

Given,

16x2-9=0

First look for a common factor (GCF) of the terms 16x2, -9.

Bur, here the GCF is 1.

Thus, we have

16x2-9=0

4·4x2-3·3=0

42x2-32=0

4x2-32=0

Now, factor the above equation by using the property of the difference of squares of a binomial a2-b2=a-b(a+b).

Here,

a=4x, and

b=3

Thus,

4x-34x+3=0

By the Zero product property,

4x-3=0 or 4x+3=

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