Chapter 4, Problem 10AR

To determine

To Solve: The quadratic equation $49z^2=1$ using factoring or quadratic formula.

Answer to Problem 10AR

The solution of equation is either $z=\frac{1}{7}$ or $z=-\frac{1}{7}$ .

Explanation of Solution

Given information:

The quadratic equation $49z^2=1$

Concept and Formula Used:

Quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where quadratic equation is $a{x}^2+bx+c=0$

Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Calculation:

It is given that

  $49z^2=1$

The equation can be written as

  $49z^2-1=0$

Solving equation using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where $a=49,b=0\&c=-1$

Putting the values in the formula

  $\begin{array}{l}z=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(49\right)\times \left(-1\right)}}{2\left(49\right)}\\ z=\frac{0\pm \sqrt{196}}{98}\\ z=\frac{\pm \sqrt{196}}{98}\\ z=\frac{\pm 14}{98}\end{array}$

Therefore either $z=\frac{14}{98}=\frac{1}{7}$ or $z=-\frac{14}{96}=-\frac{1}{7}$

Either $z=\frac{1}{7}$ or $z=-\frac{1}{7}$

Conclusion:

The solution of equation is either $z=\frac{1}{7}$ or $z=-\frac{1}{7}$ .