Chapter 4, Problem 7AR

To determine

To Solve: The quadratic equation $n^2-144=25$ using factoring or quadratic formula.

Answer to Problem 7AR

The solution of equation is either $n=13$ or $n=-13$ .

Explanation of Solution

Given information:

The quadratic equation $n^2-144=25$

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

  $n^2-144=25$

The equation can be written as

  $\begin{array}{l}{n}^2-144-25=0\\ n^2-169=0\end{array}$

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

Where $a=1,b=0\&c=-169$

Putting the values in the formula

  $\begin{array}{l}n=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(1\right)\times \left(-169\right)}}{2\left(1\right)}\\ n=\frac{0\pm \sqrt{676}}{2}\\ n=\frac{\pm \sqrt{676}}{2}\\ n=\pm \frac{26}{2}\end{array}$

Therefore either $n=\frac{26}{2}$ or $n=-\frac{26}{2}$

Either $n=13$ or $n=-13$

Conclusion:

The solution of equation is either $n=13$ or $n=-13$ .