Chapter 4.3, Problem 41PPS

To determine

To calculate: The solution of the equation $x^2+13=17$ by factoring.

Answer to Problem 41PPS

The solution of the equation is $-2\text{ and 2}$ .

Explanation of Solution

Given information:

The equation $x^2+13=17$ .

Formula used:

Solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

Calculation:

Consider the given equation $x^2+13=17$ .

Recall that solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

So, $x^2+13=17$ will be factorized as,

  $\begin{array}{c}{x}^2+13=17\\ x^2+13-17=0\\ x^2-4=0\\ \left(x+2\right)\left(x-2\right)=0\end{array}$ .

Therefore, either $\begin{array}{c}x-2=0\text{ or }x+2=0\\ x=2\text{ or }x=-2\end{array}$ .

Thus, the solution of the equation is $-2\text{ and 2}$ .