Chapter 12.5, Problem 1WE

To determine

Solve the quadratic equation.

Answer to Problem 1WE

  $x\in \left\{1,-6\right\}$

Explanation of Solution

Given:

The equation is :

  $x^2+5x-6=0$

Calculation:

The given equation $x^2+5x-6=0$ is of the type $a{x}^2+bx+c=0$ , where a = 1 , b = 5, c = -6

  $b^2-4ac={(5)}^2-4(1)(-6)=25+24=49$ , which is perfect square .

So, it can be solved by factoring the middle term.

  $\begin{array}{l}{x}^2+5x-6=0\\ \Rightarrow x^2+6x-x-6=0\\ \Rightarrow x(x+6)-1(x+6)=0\\ \Rightarrow (x-1)(x+6)=0\\ \Rightarrow x-1=0\text{ and }x+6=0\\ \Rightarrow x=1\text{ and }x=-6\end{array}$

So, $x\in \left\{1,-6\right\}$