Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with$a\ne 0$, then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$n^2-144=25$

Short answer

The values of n are$n=13$and$n=-13$.

Step-by-step solution

- Understand the concept used 

If $a{x}^2+bx+c=0$, with,$a\ne 0$ then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that$n^2-144=25$can be written as

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

Using quadratic formula$n=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for a, 0 for b and -169 for c.

Put the values in the formula and get $n=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(1\right)\times (-169)}}{2\left(1\right)}$.

- Simplify for n 

Simplify the expression for n.

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

Therefore, either$n=\frac{26}{2}$ or$n=-\frac{26}{2}$ that is., either $n=13$or$n=-13$ .