Chapter MPS, Problem 5.4MPS

To determine

To Find: The integer.

Answer to Problem 5.4MPS

  $x=-7orx=6$

Explanation of Solution

Given:

  $\begin{array}{l}letusassumethenumber=x\\ Nowx+x^2=42\end{array}$

Formula Used:

  $\begin{array}{l}y\left(x\right)=a{x}^2+bx+c=\left(x+c\right)\left(x+d\right)\end{array}$

Calculation:

  $\begin{array}{l}{x}^2+x=42\\ \text{⇒}x+x^2-42=0\\ \text{⇒}\left(x+7\right)\left(x-6\right)=0\\ \text{⇒}x=-7orx=6\end{array}$

Conclusion:

Thus the required integer is $x=-7orx=6$ .