Chapter 1.4, Problem 32E

Solution

To solve: The equation $16x^2-1=0$ .

  $x=-\frac{1}{4}$ , $x=\frac{1}{4}$ .

Given information:

The equation, $16x^2-1=0$ .

Concept used:

Zero product property: If $ab=0$ , then either $a=0$ or $b=0$ , or both $a=0$ , $b=0$ .

Calculation:

Solve the given equation as follows:

  $\begin{array}{c}16x^2-1=0\\ {\left(4x\right)}^2-1^2=0\\ \left(4x+1\right)\left(4x-1\right)=0\\ \begin{array}{ccc}4x+1=0& \text{or}& 4x-1=0\\ 4x=-1& \text{or}& 4x=1\\ x=-\frac{1}{4}& \text{or}& x=\frac{1}{4}\end{array}\end{array}$

Conclusion:

The solution of the equation $16x^2-1=0$ are $x=-\frac{1}{4}$ and $x=\frac{1}{4}$ .