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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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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